Free Printable DE Diagnostic Test

1.

$\frac{d}{dx}\left(2\ \sin\ 3x\right)$

a)

$2\ \cos\ 3x$

b)

$3\ \cos\ 3x$

c)

$6\ \cos\ 3x$

d)

$-6\ \cos\ 3x$

2.

$\frac{d}{dx}\left(2x^3-\frac{4}{\ x^2}\right)$

a)

$6x^2-\frac{8}{x}$

b)

$2x^2-\frac{4}{x}$

c)

$6x^2+\frac{8}{x}$

d)

$3x^2+\frac{4}{x}$

3.

Find dy/dx:

y=\sin\ (\ln\ x^2)

a)

$2\ \cos\ \ln\ x^2$

b)

$\frac{2\ \cos\ \left(\ln\ x^2\right)}{x}$

c)

$2x\ \cos\ \left(\ln\ x^2\right)$

d)

$2\ \cos\ \left(\ln\ x^2\right)$

4.

Find dy/dx:

y=\sin\ (\ln\ x^2)

a)

$2\ \cos\ \ln\ x^2$

b)

$\frac{2\ \cos\ \left(\ln\ x^2\right)}{x}$

c)

$2x\ \cos\ \left(\ln\ x^2\right)$

d)

$2\ \cos\ \left(\ln\ x^2\right)$

5.

If the first derivative of a function is a constant, then the function is

a)

linear

b)

quadratic

c)

exponential

d)

cunic

6.

$\frac{d}{dx}\left(\ln\ \cos\ x\right)$

a)

$\sec\ x$

b)

$-\tan\ x$

c)

$-\sec\ x$

d)

$\tan\ x$

7.

$\frac{d}{dx}\left(\tan\ 4x\right)$

a)

$4\ \sec\ 4x$

b)

$4\ \sec^24x$

c)

$\sec^24x$

d)

$4\ \sec4x\ \tan\ 4x$

8.

$\frac{d}{dx}\left(\sqrt{4x+1}\right)$

a)

$2\sqrt{4x+1}$

b)

$4\sqrt{4x+1}$

c)

$\frac{4}{\sqrt{4x+1}}$

d)

$\frac{2}{\sqrt{4x+1}}$

9.

$\frac{d}{dx}\left(2e^{-0.5x}\right)$

a)

$e^{-0.5x}$

b)

$-e^{-0.5x}$

c)

$2e^{-0.5x}$

d)

$-2e^{-0.5x}$

10.

$\frac{d}{dx}\left(\tan^{-1}5x\right)$

a)

$\frac{5}{1+25x^2}$

b)

$\frac{1}{1+5x^2}$

c)

$\frac{1}{1+25x^2}$

d)

$\frac{5}{1+5x^2}$

11.

Given that

x=t^2+2t

and

y=2t^3-6t

, Find

\frac{dy}{dx}

a)

$\frac{3t^2-6}{2t+2}$

b)

$\left(2t+2\right)\left(6t^2-6\right)$

c)

$\frac{6t^2-6}{2t+2}$

d)

$\frac{2t+2}{6t^2-6}$

12.

$\frac{d}{dx}\left(\frac{2x}{\sqrt{x^2-4}}\right)$

a)

$\frac{2x^2}{\sqrt{x^2-4}}$

b)

$-\frac{8}{\sqrt{\left(x^2-4\right)^3}}$

c)

$-\frac{8}{\sqrt{x^2-4}}$

d)

$\frac{2x^2-4}{\sqrt{\left(x^2-4\right)^3}}$

13.

$\int e^{-2x}dx$

a)

$2e^x+C$

b)

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

c)

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

d)

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

14.

$\int\ \frac{dx}{4-x}$

a)

$\ln\ \left(4-x\right)+C$

b)

$-\ln\left(4-x\right)+C$

c)

$\frac{1}{4}\ln\left(4-x\right)+C$

d)

$\frac{1}{2}\ln\left(4-x\right)+C$

15.

$\int xe^x\ dx$

a)

$xe^x-1+C$

b)

$e^x\left(x-1\right)+C$

c)

$xe^x-x+C$

d)

$e^x-x+C$

16.

$\int\ln\ x\ dx$

a)

$x\ \ln\ x-x\ +C$

b)

$x\ \ln\ x\ -\ 1\ +C$

c)

$\ln\ x\ -\ 1+C$

d)

$x\ \ln\ x+1+C$

17.

$\int6e^{3x}dx$

a)

$2e^{3x}+C$

b)

$\frac{1}{3}e^{3x}+C$

c)

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

d)

$3e^{3x}+C$

18.

$\int\ \frac{dx}{9+4x^2}$

a)

$\frac{1}{2}\tan^{-1}\left(\frac{2x}{3}\right)+C$

b)

$\frac{1}{3}\tan^{-1}\left(\frac{2x}{3}\right)+C$

c)

$\frac{1}{6}\tan^{-1}\left(\frac{2x}{3}\right)+C$

d)

$\frac{1}{3}\tan^{-1}\left(\frac{2x}{9}\right)+C$

19.

$\int\ \frac{dx}{\sqrt{4-x^2}}$

a)

$\sin^{-1}\left(\frac{x}{2}\right)+C$

b)

$\frac{1}{2}\sin^{-1}x+C$

c)

$\sin^{-1}x+C$

d)

$\sin^{-1}\left(\frac{x}{4}\right)+C$

20.

$\int\sec\ t\ dt$

a)

$\sec t\tan t+C$

b)

$\sec t+\tan t+C$

c)

$\ln\left|\sec\tan t\right|+C$

d)

$\ln\left|\sec t+\tan t\right|+C$

21.

$\int\ \frac{4dx}{\sqrt{2x+1}}$

a)

$2\sqrt{2x+1}+C$

b)

$4\sqrt{2x+1}+C$

c)

$\frac{1}{4}\sqrt{2x+1}+C$

d)

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

22.

$\int\csc x\ \cot x\ dx$

a)

$\csc\ x\ +C$

b)

$-\csc\ x+C$

c)

$\cot\ x+C$

d)

$-\cot x+C$

23.

$\int\csc^2x\ dx$

a)

$-\cot x+C$

b)

$-\cot x\csc x+C$

c)

$\cot x+C$

d)

$\cot x\csc x+C$

24.

$\int\cos\ 2x\ dx$

a)

$\frac{1}{2}\sin2x+C$

b)

$2\ \sin\ 2x+C$

c)

$-\frac{1}{2}\sin2x+C$

d)

$-2\ \sin\ 2x+C$

25.

$\int\left(2x+5\right)^3dx$

a)

$\frac{1}{4}\left(2x+5\right)^4+C$

b)

$\frac{1}{8}\left(2x+5\right)^4+C$

c)

$\frac{1}{2}\left(2x+5\right)^4+C$

d)

$\left(2x+5\right)^4+C$

26.

$\int20x^3\ dx$

a)

$4x^4+C$

b)

$5x^4+C$

c)

$10x^4+C$

d)

$20x^4+C$

27.

$\int\cos^2\ t\ \sin t\ dt$

a)

$\frac{1}{3}\cos^3t+C$

b)

$-\frac{1}{3}\cos^3t+C$

c)

$3\cos^3t+C$

d)

$-3\cos^3t+C$

28.

$\int\sin\ 2x\ dx$

a)

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

b)

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

c)

$2\cos\ 2x+C$

d)

$-2\cos\ 2x+C$

29.

What is the Integration by Parts Formula?

a)

b)

c)

d)

30.

What would you choose for your u here if you used integration by parts?

a)

t

b)

3t

c)

e^2t

d)

e^t

e)

don't use IBP, let u = 2t

DE Diagnostic Test

Total questions: 30

Worksheet time: 15mins

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