Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
A =
6
6
6
s^
2
2
2
View step-by-step help
Home
Math Problems
Calculus
Find derivatives of trigonometric functions using the product and quotient rules
Full solution
Q.
A =
6
6
6
s^
2
2
2
Identify Function:
Identify the function to differentiate. A =
6
s
2
6s^2
6
s
2
Apply Power Rule:
Apply the power rule for differentiation.
d
d
s
[
6
s
2
]
=
6
⋅
d
d
s
[
s
2
]
\frac{d}{ds} [6s^2] = 6 \cdot \frac{d}{ds} [s^2]
d
s
d
[
6
s
2
]
=
6
⋅
d
s
d
[
s
2
]
Differentiate
s
2
s^2
s
2
:
Differentiate
s
2
s^2
s
2
using the power rule.
d
d
s
[
s
2
]
=
2
s
\frac{d}{ds} [s^2] = 2s
d
s
d
[
s
2
]
=
2
s
Multiply Constant:
Multiply the constant
6
6
6
by the derivative of
s
2
s^2
s
2
.
6
∗
2
s
=
12
s
6 * 2s = 12s
6
∗
2
s
=
12
s
More problems from Find derivatives of trigonometric functions using the product and quotient rules
Question
Find
lim
θ
→
π
2
tan
2
(
θ
)
[
1
−
sin
(
θ
)
]
\lim_{\theta \rightarrow \frac{\pi}{2}} \tan ^{2}(\theta)[1-\sin (\theta)]
lim
θ
→
2
π
tan
2
(
θ
)
[
1
−
sin
(
θ
)]
.
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
1
2
\frac{1}{2}
2
1
\newline
(C)
−
2
-2
−
2
\newline
(D) The limit doesn't exist
Get tutor help
Posted 7 months ago
Question
Find
lim
θ
→
π
2
sin
2
(
2
θ
)
1
−
sin
2
(
θ
)
\lim _{\theta \rightarrow \frac{\pi}{2}} \frac{\sin ^{2}(2 \theta)}{1-\sin ^{2}(\theta)}
lim
θ
→
2
π
1
−
s
i
n
2
(
θ
)
s
i
n
2
(
2
θ
)
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
2
2
2
\newline
(C)
4
4
4
\newline
(D) The limit doesn't exist
Get tutor help
Posted 7 months ago
Question
Find
lim
x
→
3
x
−
3
4
x
+
4
−
4
\lim _{x \rightarrow 3} \frac{x-3}{\sqrt{4 x+4}-4}
lim
x
→
3
4
x
+
4
−
4
x
−
3
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
4
-4
−
4
\newline
(B)
1
1
1
\newline
(C)
2
2
2
\newline
(D) The limit doesn't exist
Get tutor help
Posted 7 months ago
Question
Find
lim
x
→
−
4
7
x
+
28
x
2
+
x
−
12
\lim _{x \rightarrow-4} \frac{7 x+28}{x^{2}+x-12}
lim
x
→
−
4
x
2
+
x
−
12
7
x
+
28
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
7
7
7
\newline
(C)
−
1
-1
−
1
\newline
(D) The limit doesn't exist
Get tutor help
Posted 7 months ago
Question
Find
lim
x
→
−
3
x
+
3
4
−
2
x
+
22
\lim _{x \rightarrow-3} \frac{x+3}{4-\sqrt{2 x+22}}
lim
x
→
−
3
4
−
2
x
+
22
x
+
3
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
3
-3
−
3
\newline
(B)
−
4
-4
−
4
\newline
(C)
−
3
4
-\frac{3}{4}
−
4
3
\newline
(D) The limit doesn't exist
Get tutor help
Posted 7 months ago
Question
Find
lim
x
→
1
5
x
+
4
−
3
x
−
1
\lim _{x \rightarrow 1} \frac{\sqrt{5 x+4}-3}{x-1}
lim
x
→
1
x
−
1
5
x
+
4
−
3
.
\newline
Choose
1
1
1
answer:
\newline
(A)
3
5
\frac{3}{5}
5
3
\newline
(B)
5
6
\frac{5}{6}
6
5
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist
Get tutor help
Posted 7 months ago
Question
Find
lim
x
→
−
2
x
3
+
3
x
2
+
2
x
x
+
2
\lim _{x \rightarrow-2} \frac{x^{3}+3 x^{2}+2 x}{x+2}
lim
x
→
−
2
x
+
2
x
3
+
3
x
2
+
2
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
6
6
6
\newline
(B)
0
0
0
\newline
(C)
2
2
2
\newline
(D) The limit doesn't exist
Get tutor help
Posted 7 months ago
Question
Find
lim
x
→
π
2
cot
2
(
x
)
1
−
sin
(
x
)
\lim _{x \rightarrow \frac{\pi}{2}} \frac{\cot ^{2}(x)}{1-\sin (x)}
lim
x
→
2
π
1
−
s
i
n
(
x
)
c
o
t
2
(
x
)
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
−
π
2
-\frac{\pi}{2}
−
2
π
\newline
(C)
2
2
2
\newline
(D) The limit doesn't exist
Get tutor help
Posted 7 months ago
Question
Find
lim
x
→
π
2
sin
(
2
x
)
cos
(
x
)
\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sin (2 x)}{\cos (x)}
lim
x
→
2
π
c
o
s
(
x
)
s
i
n
(
2
x
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
2
\frac{1}{2}
2
1
\newline
(B)
1
1
1
\newline
(C)
2
2
2
\newline
(D) The limit doesn't exist
Get tutor help
Posted 7 months ago
Question
Find
lim
θ
→
π
4
cos
(
2
θ
)
2
cos
(
θ
)
−
1
\lim _{\theta \rightarrow \frac{\pi}{4}} \frac{\cos (2 \theta)}{\sqrt{2} \cos (\theta)-1}
lim
θ
→
4
π
2
c
o
s
(
θ
)
−
1
c
o
s
(
2
θ
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
2
2
2
\newline
(B)
1
2
\frac{1}{2}
2
1
\newline
(C)
2
\sqrt{2}
2
\newline
(D) The limit doesn't exist
Get tutor help
Posted 7 months ago
Related topics
Algebra - Order of Operations
Algebra - Distributive Property
`X` and `Y` Axes
Geometry - Scalene Triangle
Common Multiple
Geometry - Quadrant