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Math Problems
Calculus
Find derivatives of radical functions
A = \frac{
1
1
1
}{
2
2
2
}(b+c)h
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Using implicit differentiation, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
.
\newline
x
y
=
−
2
+
y
x
3
\sqrt{x y}=-2+y x^{3}
x
y
=
−
2
+
y
x
3
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Differentiate
d
y
d
x
=
e
x
+
y
\frac{d y}{d x}=e^{x+y}
d
x
d
y
=
e
x
+
y
with initial condition
y
(
0
)
=
−
ln
3
y(0)=-\ln 3
y
(
0
)
=
−
ln
3
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Find
f
′
(
x
)
f'(x)
f
′
(
x
)
where
f
(
x
)
=
3
x
cos
(
x
)
f(x)=3x\cos(x)
f
(
x
)
=
3
x
cos
(
x
)
.
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Using implicit differentiation, find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
.
sin
(
x
y
)
=
2
x
4
y
3
+
4
\sin(xy) = 2x^{4}y^{3} + 4
sin
(
x
y
)
=
2
x
4
y
3
+
4
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If
(
x
,
y
)
(x,y)
(
x
,
y
)
satisfies the given system of equations, what is the value of
x
x
x
?
\newline
2
y
−
x
=
0
,
x
=
y
+
7
\begin{align*} 2y - x &= 0, \ & x = y + 7 \end{align*}
2
y
−
x
=
0
,
x
=
y
+
7
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Find the
y
y
y
-coordinate of the
y
y
y
-intercept of the polynomial function defined below.
\newline
f
(
x
)
=
8
x
+
5
−
2
x
2
f(x)=8 x+5-2 x^{2}
f
(
x
)
=
8
x
+
5
−
2
x
2
\newline
Answer:
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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an
(
x
,
y
)
(x, y)
(
x
,
y
)
point.
\newline
y
=
−
x
2
+
2
x
+
7
y=-x^{2}+2 x+7
y
=
−
x
2
+
2
x
+
7
\newline
Answer:
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Find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
for the given function.
\newline
y
=
x
2
−
csc
(
x
)
+
5
y=x^{2}-\csc(x)+5
y
=
x
2
−
csc
(
x
)
+
5
\newline
d
y
d
x
=
\frac{dy}{dx}=
d
x
d
y
=
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Find the derivative of the function.
\newline
G
(
z
)
=
(
1
−
9
z
)
2
z
2
+
1
G(z)=(1-9z)^{2}\sqrt{z^{2}+1}
G
(
z
)
=
(
1
−
9
z
)
2
z
2
+
1
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Find the derivative of the following function.
\newline
y
=
9
−
x
2
y=9^{-x^{2}}
y
=
9
−
x
2
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
9
5
x
3
+
4
x
2
y=9^{5 x^{3}+4 x^{2}}
y
=
9
5
x
3
+
4
x
2
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
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Find the derivative of the following function.
\newline
y
=
2
−
x
2
y=2^{-x^{2}}
y
=
2
−
x
2
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
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Find the derivative of the following function.
\newline
y
=
8
9
x
5
−
5
x
4
y=8^{9 x^{5}-5 x^{4}}
y
=
8
9
x
5
−
5
x
4
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
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Find the derivative of the following function.
\newline
y
=
7
−
x
4
y=7^{-x^{4}}
y
=
7
−
x
4
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
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Find the derivative of the following function.
\newline
y
=
3
−
5
x
2
y=3^{-5 x^{2}}
y
=
3
−
5
x
2
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
3
−
8
x
2
y=3^{-8 x^{2}}
y
=
3
−
8
x
2
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
7
x
2
−
9
x
y=7^{x^{2}-9 x}
y
=
7
x
2
−
9
x
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
7
3
x
5
−
2
x
4
y=7^{3 x^{5}-2 x^{4}}
y
=
7
3
x
5
−
2
x
4
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
8
−
9
x
5
+
6
x
4
y=8^{-9 x^{5}+6 x^{4}}
y
=
8
−
9
x
5
+
6
x
4
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
2
−
5
x
4
y=2^{-5 x^{4}}
y
=
2
−
5
x
4
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
6
−
4
x
2
y=6^{-4 x^{2}}
y
=
6
−
4
x
2
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
3
−
9
x
4
+
3
x
3
y=3^{-9 x^{4}+3 x^{3}}
y
=
3
−
9
x
4
+
3
x
3
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
2
−
8
x
5
+
2
x
4
y=2^{-8 x^{5}+2 x^{4}}
y
=
2
−
8
x
5
+
2
x
4
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
5
8
x
2
y=5^{8 x^{2}}
y
=
5
8
x
2
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
−
6
x
6
+
3
x
5
y=e^{-6 x^{6}+3 x^{5}}
y
=
e
−
6
x
6
+
3
x
5
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
7
6
x
6
−
5
x
5
y=7^{6 x^{6}-5 x^{5}}
y
=
7
6
x
6
−
5
x
5
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
7
9
x
4
+
4
x
3
y=7^{9 x^{4}+4 x^{3}}
y
=
7
9
x
4
+
4
x
3
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
3
x
2
−
4
x
y=3^{x^{2}-4 x}
y
=
3
x
2
−
4
x
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
2
−
3
x
6
y=2^{-3 x^{6}}
y
=
2
−
3
x
6
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
−
6
x
2
+
3
x
y=e^{-6 x^{2}+3 x}
y
=
e
−
6
x
2
+
3
x
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
7
x
3
y=e^{7 x^{3}}
y
=
e
7
x
3
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
−
3
x
5
−
6
x
4
y=e^{-3 x^{5}-6 x^{4}}
y
=
e
−
3
x
5
−
6
x
4
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
x
5
−
6
x
4
y=e^{x^{5}-6 x^{4}}
y
=
e
x
5
−
6
x
4
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
−
6
x
3
+
5
x
2
y=e^{-6 x^{3}+5 x^{2}}
y
=
e
−
6
x
3
+
5
x
2
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
−
3
x
3
−
7
x
2
y=e^{-3 x^{3}-7 x^{2}}
y
=
e
−
3
x
3
−
7
x
2
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
−
6
x
2
−
9
x
y=e^{-6 x^{2}-9 x}
y
=
e
−
6
x
2
−
9
x
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
−
6
x
2
+
9
x
y=e^{-6 x^{2}+9 x}
y
=
e
−
6
x
2
+
9
x
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
x
3
+
4
x
2
y=e^{x^{3}+4 x^{2}}
y
=
e
x
3
+
4
x
2
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
−
2
x
6
y=e^{-2 x^{6}}
y
=
e
−
2
x
6
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
−
x
3
y=e^{-x^{3}}
y
=
e
−
x
3
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
−
7
x
6
y=e^{-7 x^{6}}
y
=
e
−
7
x
6
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
9
x
3
−
2
x
2
y=e^{9 x^{3}-2 x^{2}}
y
=
e
9
x
3
−
2
x
2
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
−
8
x
4
y=e^{-8 x^{4}}
y
=
e
−
8
x
4
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
e
2
x
4
y=e^{2 x^{4}}
y
=
e
2
x
4
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
ln
(
5
x
2
+
x
)
y=\ln \left(5 x^{2}+x\right)
y
=
ln
(
5
x
2
+
x
)
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
ln
(
4
x
2
−
3
x
)
y=\ln \left(4 x^{2}-3 x\right)
y
=
ln
(
4
x
2
−
3
x
)
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
ln
(
−
7
x
3
−
6
x
2
)
y=\ln \left(-7 x^{3}-6 x^{2}\right)
y
=
ln
(
−
7
x
3
−
6
x
2
)
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
ln
(
x
2
+
8
x
)
y=\ln \left(x^{2}+8 x\right)
y
=
ln
(
x
2
+
8
x
)
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
Find the derivative of the following function.
\newline
y
=
ln
(
5
x
2
)
y=\ln \left(5 x^{2}\right)
y
=
ln
(
5
x
2
)
\newline
Answer:
y
′
=
y^{\prime}=
y
′
=
Get tutor help
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