Free Printable logarithmic differentiation

1.

Find the derivative of $y=\log_9x$

a)

\frac{1}{\left(\log x\right)9}

b)

$\frac{\ln9}{x}$

c)

$\frac{1}{x\ln x}$

d)

$\frac{1}{\left(\ln9\right)x}$

2.

Differentiate

y=\frac{1}{3}\ln x

a)

3/x

b)

1/x

c)

x/3

d)

1/3x

3.

Differentiate y = ln (5x - 7)

a)

_ 5 _

5x-7

b)

_ 1 _

5x-7

c)

ln5

d)

ln5x - ln 7

4.

Differentiate y = ln (5x - 7)

a)

_ 5 _

5x-7

b)

_ 1 _

5x-7

c)

ln5

d)

ln5x - ln 7

5.

Find $\frac{dy}{dx}$ for $y=\ln\left(\frac{2x+1}{1-2x}\right)$ .

a)

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

b)

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

c)

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

d)

$\frac{2}{2x+1}+\frac{2}{1+2x}$

6.

Differentiating $\frac{\left(e^{2x}-e^x\right)^2}{e^x}$ yields:

a)

$3e^{3x}+e^x$

b)

$3e^{3x}-4e^{2x}+e^x$

c)

$e^{3x}-e^{2x}+e^x$

d)

$e^{3x}+e^x$

e)

$\frac{1}{3}e^{3x}-e^{2x}+e^x$

7.

$g\left(x\right)=\ln\left(2x^3+1\right)$

a)

$-\frac{6x^2}{2x^3+1}$

b)

$\frac{6x^2}{2x^3+1}$

c)

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

d)

$\frac{1}{2x^3+1}$

8.

Find the differentiation of $\ln\left(\sqrt{x^3+2x}\right)$

a)

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

b)

$\left(\frac{1}{2}.\frac{3x^2+2}{x^3+2x}\right)$

c)

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

9.

Find the derivative of the function below using the method of "Logarithmic Differentiation." Submit an image of your work on Schoology.

f(t) = (t² + 2t)⁵

a)

f'(t) = 5(2t+2)⁴

b)

f'(t) = 5(t² + 2t)⁴

c)

f'(t) = 5(t² + 2t)⁴(2t)

d)

f'(t) = 5(t² + 2t)⁴(2t + 2)

10.

Find the differentiation of $\ln\left(x^2+2\right)$

a)

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

b)

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

c)

$2x$

logarithmic differentiation

Total questions: 10

Worksheet time: 10mins

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