Free Printable 9.3 Differentiation of Exp, Log & Trig Functions

1.

Differentiate $y=\frac{5e^x}{3e^x+1}$ .

a)

$y=\frac{30e^{2x}}{\left(3e^x+1\right)^2}$

b)

$y=\frac{15e^{2x}}{\left(3e^x+1\right)^2}$

c)

$y=\frac{5e^x}{\left(3e^x+1\right)^2}$

d)

$y=\frac{5e^x}{\left(3e^x+1\right)^{ }}$

2.

Differentiate $f\left(x\right)=4^x-5\ln x$ .

a)

$f'\left(x\right)=4^x\ln4-\frac{5}{x}$

b)

$f'\left(x\right)=4^x\ln4-\frac{1}{x\ln5}$

c)

$f'\left(x\right)=4^x-\frac{5}{x}$

d)

$f'\left(x\right)=4^x\ln4-5x$

3.

Find the tangent of $f\left(x\right)=7^x+4e^x$ at $x=0$ .

a)

$f'\left(0\right)=11$

b)

$f'\left(0\right)=1.3863$

c)

$f'\left(0\right)=1.9459$

d)

$f'\left(0\right)=5.9459$

4.

Diifferentiate $y=x^5-e^x\ln x$ .

a)

$y'=5x^4-e^x\ln\left(x\right)-\frac{e^x}{x}$

b)

$y'=5x^4-e^x\ln\left(x\right)+\frac{e^x}{x}$

c)

$y'=5x^4-\ln\left(xe^x\right)-\frac{e^x}{x}$

d)

$y'=5x^4-\frac{\ln\left(x\right)}{e^x}-\frac{e^x}{x}$

5.

Find the derivative of $h\left(x\right)=\frac{1+4\ln\left(x\right)}{5x^3}$ .

a)

$\frac{dh}{dx}=\frac{−12\ln(x)−1}{5x^4}$

b)

$\frac{dh}{dx}=-\frac{12\ln x-1}{5x^4}$

c)

$\frac{dh}{dx}=\frac{4\ln(x)+1}{5x^6}$

d)

$\frac{dh}{dx}=-\frac{4\ln(x)+1}{5x^6}$

6.

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

.

a)

$f'\left(x\right)=\frac{1}{2}\left(\frac{3x^2+2}{x^3+2x}\right)$

b)

$f'\left(x\right)=\frac{3x^2+2}{x^3+2x}$

c)

$f'\left(x\right)=\sqrt{\left(\frac{3x^2+2}{x^3+2x}\right)}$

d)

$f'\left(x\right)=\frac{1}{2}\left(\frac{x^3+2x}{3x^2+2}\right)$

7.

Determine the derivative of $y=\ln\left(\frac{2x+1}{1-2x}\right)$ .

a)

$y'=\frac{1}{2x+1}-\frac{1}{1-2x}$

b)

$y'=\frac{1}{2x+1}+\frac{1}{1-2x}$

c)

$y'=\frac{2}{2x+1}-\frac{2}{1-2x}$

d)

$y'=\frac{2}{2x+1}+\frac{2}{1-2x}$

8.

Differentiate $g\left(x\right)=3\sec\left(x\right)-10\cot\left(x\right)$ .

a)

$g'\left(x\right)=3\sec\left(x\right)\tan\left(x\right)+10\csc^2\left(x\right)$

b)

$g'\left(x\right)=3\sec\left(x\right)-10\csc^2\left(x\right)$

c)

$g'\left(x\right)=3\sec\left(x\right)\tan\left(x\right)-10\csc^2\left(x\right)$

d)

$g'\left(x\right)=3\sec\left(x\right)+10\csc^2\left(x\right)$

9.

Find the derivative of $h\left(x\right)=\frac{\sin x}{3-2\cos x}$ .

a)

$h'\left(x\right)=\frac{−2\cos^2x−2\sin^2x}{\left(3−2\cos x\right)^2}$

b)

$h'\left(x\right)=\frac{3\cos x−2\cos^2x−2\sin^2x}{\left(3−2\cos x\right)^2}$

c)

$h'\left(x\right)=\frac{3\cos x−2}{\left(3−2\cos x\right)^2}$

d)

$h'\left(x\right)=\frac{3\cos x}{\left(3−2\cos x\right)^2}$

10.

Differentiate $y=6+4\sqrt{x}\csc\left(x\right)$ .

a)

$y'=2x^{-\frac{1}{2}}\csc\left(x\right)-4\sqrt{x}\cot\left(x\right)\csc\left(x\right)$

b)

$y'=2x^{-\frac{1}{2}}\csc\left(x\right)-4\sqrt{x}\csc\left(x\right)$

c)

$y'=2x^{\frac{1}{2}}\csc\left(x\right)-4x^{-\frac{1}{2}}\cot\left(x\right)\csc\left(x\right)$

d)

$y'=2x^{-\frac{1}{2}}\csc\left(x\right)-4x^{-\frac{1}{2}}\csc\left(x\right)$

9.3 Differentiation of Exp, Log & Trig Functions

Total questions: 10

Worksheet time: 2hrs 40mins

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