Free Printable Derivative of Exponential and Logarithmic Functions

1.

Find the derivative:

y=log₉x

a)

y′=1 /((log9)x)

b)

y′=(ln9)/x

c)

y′=1/(x(lnx))

d)

y′=1/((ln9)x)

2.

Find the derivative:

y=(2^3x+4)

a)

3(ln2)(2^3x+4)

b)

3(2^3x+4)

c)

3(2^3x+4/(ln2))

d)

2^3x+4

3.

Find the derivative f(x) = xe^x

a)

f'(x) = e^x

b)

f'(x) = xe^x + xe^x

c)

f'(x) = e^x - xe^x

d)

f'(x) = e^x + xe^x

4.

Find the derivative:

y=log₄(6x+5))

a)

(ln4)(1/(6x+5))

b)

(6ln4)/(6x+5)

c)

6/((ln4)(6x+5))

d)

6/(6x+5)

5.

Find the derivative:
y=4e^x²

a)

y'=8xe^x

b)

y'=8xe^x²

c)

y'=8xe^2x

d)

y'=8xe^4x²

6.

Find the derivative:

y=e^5x+ln(x)

a)

e^5+1/x

b)

e^5x+ln(x)

c)

(5+1/x) e^5x+ln(x)

d)

(5/x) e^5x+ln(x)

7.

Find the derivative:
y = 3ln(x²-3)

a)

6x/(x²-3)

b)

3/(x²-3)

c)

3x/(x²-3)

d)

9x/(x²-3)

8.

Find the derivative:

y=ln(3x²-5x)

a)

(6x-5)/(3x²-5)

b)

6x-5

c)

(x³/3)-(5x²)/2

d)

(6x-5)/(3x³-2x)

9.

a)

1/(3x²+5)^1/4

b)

(3x)/(2(3x²+5))

c)

(2(3x²+5)^3/4)/(3x)

d)

(3x²+5)^1/4

10.

Find the derivative:
y=5x²e^3x

a)

y'=10xe^3x(2x+3)

b)

y'=5xe^3x(3x+2)

c)

y'=10ex^3x(3x+2)

d)

y'=5xe^3x(2x+3)

11.

Find the derivative:
y=5x²e^3x

a)

y'=10xe^3x(2x+3)

b)

y'=5xe^3x(3x+2)

c)

y'=10ex^3x(3x+2)

d)

y'=5xe^3x(2x+3)

12.

Find the derivative f(x) = x²/e^x

a)

f'(x) = (x²e^x - 2xe^x) / (e^x)²

b)

f'(x) = (2xe^x + x²e^x) / (e^x)²

c)

f'(x) = (2xe^x - x²e^x) / (e^x)²

d)

f'(x) = x²e^x + 2xe^x

13.

$y=e^{4x}?$ Find the derivative of

a)

$e^{4x}$

b)

$\frac{e^{4x}}{4}$

c)

$4e^{4x}$

d)

$-4e^{4x}$

14.

Differentiate $f\left(x\right)\ =2xe^{mx}$

a)

$2xe^{mx}+2me^{mx}$

b)

$2\left(e^{mx}+mxe^{mx}\right)$

c)

$2mxe^{mx}$

d)

$2e^{mx}+mxe^{mx}$

15.

Differentiate $y=\ e^{\sin\left(2x\right)}+\ e^{\cos\left(2x\right)}$

a)

$e^{\sin\left(2x\right)}\cos\left(2x\right)-e^{\cos\left(2x\right)}\sin\left(2x\right)$

b)

$2e^{\sin\left(2x\right)}\cos\left(2x\right)-e^{\cos\left(2x\right)}\sin\left(2x\right)$

c)

$2e^{\sin\left(2x\right)}\cos\left(2x\right)-2e^{\cos\left(2x\right)}\sin\left(2x\right)$

d)

$-2e^{\sin\left(2x\right)}\cos\left(2x\right)+2e^{\cos\left(2x\right)}\sin\left(2x\right)$

16.

$y=\frac{4e^{3x}-e^x}{e^x}$

Find the derivative of

a)

$8e^{2x}$

b)

$4e^{2x}$

c)

$4e^{2x}-1$

d)

$8e^{2x}-1$

17.

$If\ y\ =5^{2x^2-x},\ find\ \frac{dy}{dx}.$

a)

$5^{2x^2-x}\ln\ 5$

b)

$4x\left(5^{2x^2-x}\ln\ 5\right)$

c)

$\left(2x^2-x\right)5^{2x^2-x}\ln5$

d)

$\left(4x-1\right)5^{2x^2-x}\ln\ 5$

18.

$y\ =\ln\left(2x^3+6\right)$

Differentiate.

a)

$\frac{6x^2}{x^3+3}$

b)

$\frac{2x^2}{x^3+3}$

c)

$\frac{3x^2}{x^3+3}$

d)

$\frac{3x^2}{2x^3+6}$

19.

$f\left(x\right)\ =\log_4\left(6x\right)$

Differentiate

a)

$\frac{1}{x\ln4}$

b)

$\frac{6}{x\ln4}$

c)

$\frac{1}{6x\ln4}$

d)

$\frac{6x}{\ln4}$

20.

Differentiating $-\log_e\left(2x-3\right)$ yields:

a)

$\frac{2}{2x-3}$

b)

$\frac{-1}{2x-3}$

c)

$\frac{1}{2x-3}$

d)

$\frac{2}{3-2x}$

e)

$\frac{-3}{2x-3}$

Derivative of Exponential and Logarithmic Functions

Total questions: 20

Worksheet time: 1hrs 24mins

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