Free Printable Calculus 1 Quiz 1 - Final Term (USTP

1.

Find the derivative of the given function:

f\left(x\right)=2\cos^{-1}\sqrt{x}

a)

$\frac{-1}{\sqrt{x-x^2}}$

b)

$\frac{1}{\sqrt{x-x^2}}$

c)

$\frac{-1}{\sqrt{1-x^2}}$

d)

$\frac{-1}{\sqrt{x^2-x}}$

2.

Find the derivative of the function:

h\left(y\right)=y\sin^{-1}2y

a)

$\frac{y}{\sqrt{1-4y^2}}+\sin^{-1}2y$

b)

$\frac{2y}{\sqrt{1-4y^2}}-\sin^{-1}2y$

c)

$\frac{-2y}{\sqrt{1-4y^2}}+\sin^{-1}2y$

d)

$\frac{2y}{\sqrt{1-4y^2}}+\sin^{-1}2y$

3.

Find the derivative of the following function:

f\left(x\right)=\cos^{-1}\left(\sin x\right)

a)

$\frac{\cos x}{\sin x}$

b)

$-1$

c)

$\cos x$

d)

$-\sin x$

4.

Find y':

y=4\sin^{-1}\left(\frac{1}{2}x\right)+x\sqrt{4-x^2}

a)

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

b)

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

c)

$\sqrt{4-x^2}$

d)

$\sqrt{4+x^2}$

5.

Find f'(x):

f\left(x\right)=\csc^{-1}\left(2e^{3x}\right)

a)

$\frac{-1}{\sqrt{4e^{3x}-1}}$

b)

$\frac{3}{\sqrt{4e^{6x}-1}}$

c)

$\frac{-3}{\sqrt{4e^{6x}-1}}$

d)

$\frac{-3}{\sqrt{4e^x-1}}$

6.

Find the derivative of the function:

f\left(x\right)=\tanh\ \frac{4x+1}{5}

a)

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

b)

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

c)

$-\frac{4}{5}\operatorname{sech}^2\left(\frac{4x+1}{5a}\right)$

d)

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

7.

Find y':

y=\sinh\ e^{2y}

a)

$-2e^{2y}\cosh\ e^{2y}$

b)

$2e^{2y}\cosh\ e^{2y}$

c)

$-2e^{2y}\cos\ e^{2y}$

d)

$-2e^{2y}\operatorname{sech}\ e^{2y}$

8.

Find y' :

y=\sinh^{-1}x^2

a)

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

b)

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

c)

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

d)

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

9.

Find y':

y=\tanh^{-1}\left(\cosh e^x\right)

a)

$-\csc e^x$

b)

$e^x\csc e^x$

c)

$-e^x\csc e^x$

d)

$-\frac{e^x}{\csc e^x}$

10.

A mathematician went insane and believed that he was the differentiation operator. His friends had him placed in a mental hospital until he got better. All day he would go around frightening the other patients by staring at them and saying "I differentiate you!"

One day he met a new patient; and true to form he stared at him and said "I differentiate you!", but for once, his victim's expression didn't change.

Surprised, the mathematician marshalled his energies, stared fiercely at the new patient and said loudly "I differentiate you!", but still the other man had no reaction. Finally, in frustration, the mathematician screamed out "I DIFFERENTIATE YOU!"

The new patient calmly looked up and said, "You can differentiate me all you like: I'm ______ to the x."

a)

ln

b)

e

c)

x

d)

y

11.

$\frac{\text{d}}{\text{d}y}\left(e^x\right)$

a)

$e^x$

b)

$-e^x$

c)

$\frac{1}{e^x}$

d)

$-\frac{1}{e^x}$

12.

$\frac{\text{d}}{\text{d}y}\left(e^{\left(3x+2\right)}\right)$

a)

$3e^{\left(3x+2\right)}$

b)

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

c)

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

d)

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

13.

$\frac{\text{d}}{\text{d}y}\left(x^3-2xe^x\right)$

a)

$3x^2-2e^x\left(x+1\right)$

b)

$3x^2-2\left(e^x+\frac{x}{e^x}\right)$

c)

$3x^2-2xe^x\left(2x+1\right)$

d)

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

14.

$\frac{\text{d}}{\text{d}y}\left(e^{\left(2x+1\right)}\right)^2$

a)

$4e^{\left(4x+2\right)}$

b)

$\frac{4}{e^{\left(4x+2\right)}}$

c)

$e^{\left(4x+2\right)}\left(8x^2+2x\right)$

d)

$\frac{\left(8x^2+2x\right)}{e^{\left(4x+2\right)}}$

15.

$\frac{\text{d}}{\text{d}y}\left(\frac{e^{3x}}{\sin\left(2x\right)}\right)$

a)

$\frac{e^{3x}\left(3\sin\left(2x\right)-2\cos\left(2x\right)\right)}{\sin^2\left(2x\right)}$

b)

$\frac{e^{3x}\left(2\cos\left(2x\right)-3\sin\left(2x\right)\right)}{\sin^2\left(2x\right)}$

c)

$\frac{e^{3x}\left(3\sin\left(2x\right)+2\cos\left(2x\right)\right)}{\sin^2\left(2x\right)}$

d)

$\frac{e^{3x}\left(\sin\left(2x\right)-2\cos\left(2x\right)\right)}{\sin^2\left(2x\right)}$

Calculus 1 Quiz 1 - Final Term (USTP - BSME1)

Total questions: 15

Worksheet time: 1hrs 15mins

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