Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Calculus
Find second derivatives of trigonometric, exponential, and logarithmic functions
Find the second derivative of the function.
\newline
f
(
x
)
=
4
x
−
1
−
5
x
−
4
f(x) = 4x^{-1} - 5x^{-4}
f
(
x
)
=
4
x
−
1
−
5
x
−
4
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
5
x
4
−
13
f(x) = \frac{5}{x^4} - 13
f
(
x
)
=
x
4
5
−
13
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
\_\_
__
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
2
x
+
10
f(x) = \frac{2}{x} + 10
f
(
x
)
=
x
2
+
10
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
5
x
2
+
5
x
−
1
f(x) = 5x^2 + 5x^{-1}
f
(
x
)
=
5
x
2
+
5
x
−
1
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
2
x
7
+
3
x
−
1
f(x) = -2x^7 + 3x^{-1}
f
(
x
)
=
−
2
x
7
+
3
x
−
1
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
4
x
4
−
11
f(x) = -\frac{4}{x^4} - 11
f
(
x
)
=
−
x
4
4
−
11
\newline
x
x
x
= ______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
4
x
3
+
8
f(x) = \frac{4}{x^3} + 8
f
(
x
)
=
x
3
4
+
8
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
5
x
2
+
17
f(x) = \frac{5}{x^2} + 17
f
(
x
)
=
x
2
5
+
17
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
4
x
3
+
2
x
4
f(x) = -\frac{4}{x^3} + \frac{2}{x^4}
f
(
x
)
=
−
x
3
4
+
x
4
2
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
2
x
3
+
7
f(x) = -\frac{2}{x^3} + 7
f
(
x
)
=
−
x
3
2
+
7
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
2
x
5
+
3
x
−
2
f(x) = 2x^5 + 3x^{-2}
f
(
x
)
=
2
x
5
+
3
x
−
2
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
3
x
2
+
5
x
−
2
f(x) = -3x^2 + 5x^{-2}
f
(
x
)
=
−
3
x
2
+
5
x
−
2
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
3
x
4
+
2
f(x) = \frac{3}{x^4} + 2
f
(
x
)
=
x
4
3
+
2
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
5
x
+
3
x
3
f(x) = \frac{5}{x} + \frac{3}{x^3}
f
(
x
)
=
x
5
+
x
3
3
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
4
x
−
2
−
3
x
−
4
f(x) = 4x^{-2} - 3x^{-4}
f
(
x
)
=
4
x
−
2
−
3
x
−
4
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
2
x
+
3
x
−
3
f(x) = 2x + 3x^{-3}
f
(
x
)
=
2
x
+
3
x
−
3
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
4
x
+
2
x
−
1
f(x) = 4x + 2x^{-1}
f
(
x
)
=
4
x
+
2
x
−
1
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
x
6
+
x
−
3
f(x) = x^6 + x^{-3}
f
(
x
)
=
x
6
+
x
−
3
\newline
f''(x) = ______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
3
x
7
−
x
−
3
f(x) = 3x^7 - x^{-3}
f
(
x
)
=
3
x
7
−
x
−
3
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
3
x
3
−
20
f(x) = -\frac{3}{x^3} - 20
f
(
x
)
=
−
x
3
3
−
20
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
x
4
f(x) = x^4
f
(
x
)
=
x
4
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
2
x
f(x) = 2^x
f
(
x
)
=
2
x
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
6
sin
(
x
)
f(x) = -6\sin(x)
f
(
x
)
=
−
6
sin
(
x
)
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
6
x
f(x) = 6^x
f
(
x
)
=
6
x
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
3
x
f(x) = 3^x
f
(
x
)
=
3
x
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
x
5
f(x) = x^5
f
(
x
)
=
x
5
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
3
sin
(
x
)
f(x) = -3\sin(x)
f
(
x
)
=
−
3
sin
(
x
)
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
2
sin
(
x
)
f(x) = -2\sin(x)
f
(
x
)
=
−
2
sin
(
x
)
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
x
3
f(x) = x^3
f
(
x
)
=
x
3
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
5
cos
(
x
)
f(x) = -5\cos(x)
f
(
x
)
=
−
5
cos
(
x
)
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
x
x
f(x) = x^x
f
(
x
)
=
x
x
\newline
(
x
)
=
(x) =
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
x
6
f(x) = x^6
f
(
x
)
=
x
6
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
2
sin
(
x
)
f(x) = 2\sin (x)
f
(
x
)
=
2
sin
(
x
)
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
4
x
f(x) = 4^x
f
(
x
)
=
4
x
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
5
sin
(
x
)
f(x) = -5\sin(x)
f
(
x
)
=
−
5
sin
(
x
)
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
cos
(
x
)
f(x) = -\cos (x)
f
(
x
)
=
−
cos
(
x
)
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
4
cos
(
x
)
f(x) = 4\cos (x)
f
(
x
)
=
4
cos
(
x
)
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
2
x
f(x) = -2^x
f
(
x
)
=
−
2
x
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
sin
(
x
)
f(x) = -\sin (x)
f
(
x
)
=
−
sin
(
x
)
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
Find the second derivative of the function.
\newline
f
(
x
)
=
−
3
cos
(
x
)
f(x) = -3\cos (x)
f
(
x
)
=
−
3
cos
(
x
)
\newline
f
′
′
(
x
)
=
f''(x) =
f
′′
(
x
)
=
_
_
_
_
_
_
\_\_\_\_\_\_
______
Get tutor help
The second derivative of the function
f
f
f
is defined by
f
′
′
(
x
)
=
x
2
−
5
cos
(
2
x
)
f^{\prime \prime}(x)=x^{2}-5 \cos (2 x)
f
′′
(
x
)
=
x
2
−
5
cos
(
2
x
)
for
−
2.5
<
x
<
3.5
-2.5<x<3.5
−
2.5
<
x
<
3.5
. Find the
x
x
x
-values, if any, in the given domain where the function
f
f
f
has an inflection point. You may use a calculator and round all values to
3
3
3
decimal places.
\newline
Answer:
x
=
x=
x
=
Get tutor help
