Free Printable midterm calculus honors

1.

Derivatve of secx

a)

sec²x

b)

secxtanx

c)

-secxtanx

d)

tan²x

2.

Find the derivative f(x) = (x² + 2x)⁵

a)

f'(x) = 5(2x+2)⁴

b)

f'(x) = 5(x² + 2x)⁴

c)

f'(x) = 5(x² + 2x)⁴(2x)

d)

f'(x) = 5(x² + 2x)⁴(2x + 2)

3.

Find dy/dx if y = cos⁵x

a)

5cos⁴x

b)

-5sin⁴x

c)

5(cos⁴x)sinx

d)

-5(cos⁴x)sinx

4.

Find y' if y = tan(3x²+2).

a)

sec²(3x²+2)

b)

6xsec²(3x²+2)

c)

6xsec²x(3x²+2)

d)

sec²(6x)

5.

Find f '(x) if f(x) = x⁴sinx

a)

4x³cosx

b)

x⁴cosx

c)

x⁴cosx + 4x³sinx

d)

-x⁴cosx + 4x³sinx

6.

What is f'(x) if f(x) = cos(5x⁴)?

a)

f'(x) = sin(20x³)

b)

f'(x) = 20x³ sin(5x⁴)

c)

f'(x) = -sin(20x³)

d)

f'(x) = -20x³ sin(5x⁴)

7.

Find the derivative f(x) = tan(x)cos(x)

a)

f'(x) = sec²(x)cos(x) - tan(x)sin(x)

b)

f'(x) = sec²xcos(x) + tan(x)sin(x)

c)

f'(x) = sec²(x)sin(x)

d)

f'(x) = sec²(x)cos(x )- tan(x)cos(x)

8.

Find the derivative of y = $\cos^2\left(x\right)$

a)

f'(x) = $-2\sin\left(x\right)$

b)

f'(x) = $-2\sin^2\left(x\right)$

c)

f'(x) = $2\cos\left(x\right)$

d)

f'(x) = $-2\ \cos\left(x\right)\ \sin\left(x\right)$

9.

Find the derivative f(x) = $\sqrt[]{x^2\ +1}$

a)

f'(x) = $\frac{ }{2}\frac{1}{\sqrt[]{x^2\ +1}}$

b)

f'(x) = $\frac{ }{4}\frac{x}{\sqrt[]{x^2\ +1}}$

c)

f'(x) = $\frac{x}{\sqrt[]{x^2\ +1}}$

d)

f'(x) = $\frac{4x}{\sqrt[]{x^2\ +1}}$

10.

What is f'(x) if f(x) = cos(sin(x))?

a)

f'(x) = -sin(sin(x))cos(x)

b)

f'(x) = -sin(sin(x))

c)

f'(x) = cos(sin(x))cos(x)

d)

f'(x) = -sin(x)cos(x)

11.

What is f'(x) if f(x) = cos(x)sin(x)?

a)

$f'(x)=\sin^2(x)+\cos^2(x)$

b)

$f'(x)=-\sin^2(x)+\cos^2(x)$

c)

$f'(x)=\sin^2(x)\ -\ \cos^2(x)$

d)

$f'(x)=-\sin^2(x)\cos^2(x)$

12.

What is f'(x) if $f(x)=\cos^2(\sqrt[]{x})$ ?

a)

$-\frac{\cos\left(\sqrt[]{\left(x\right)}\right)\sin\left(\sqrt[]{x}\right)}{\sqrt[]{x}}$

b)

$\frac{\cos\left(\sqrt[]{\left(x\right)}\right)\sin\left(\sqrt[]{x}\right)}{\sqrt[]{x}}$

c)

$\frac{\cos\left(\sqrt[]{\left(x\right)}\right)}{\sqrt[]{x}}$

d)

$-\cos\left(\sqrt[]{\left(x\right)}\right)\sin\left(\sqrt[]{x}\right)$

13.

What is f'(x) if $f(x)=\sqrt[]{\cos\left(x\right)}$ ?

a)

$\frac{-\sin\left(x\right)}{\sqrt[]{\cos\left(x\right)}}$

b)

$\frac{\cos\left(x\right)}{2\sqrt[]{\cos\left(x\right)}}$

c)

$\frac{-\sin\left(x\right)}{2\sqrt[]{\cos\left(x\right)}}$

d)

$\frac{-x}{2\sqrt[]{\sin\left(x\right)}}$

14.

a)

8x⁴ -60x²

b)

16x⁴

c)

(8x⁴ -60x²)/(2x²-5)²

d)

3x

15.

Given that y = (x+2)/(x-3), find y'.

a)

y' = -1/(x-3)²

b)

y' = -5/(x-3)²

c)

y' = (2x-5)/(x-3)²

d)

y' = (2x-1)/(x-3)²

16.

Find the derivative. f(x) = -8x^-3 + 5x - e^x

a)

f'(x) = -24x^-4 + 5 - e^x

b)

f'(x) = 24x^-4 + 5 - e^x

c)

f'(x) = 24x^-2 + 5 - e^x

d)

f'(x) = 24x^-4 + 5 - e^x-1

17.

Find the derivative of f(x) = x²sinx

a)

f'(x) = 2xsinx - x²cosx

b)

f'(x) = 2xsinx + x²sinx

c)

f'(x) = 2xsinx + x²cosx

d)

f'(x) = 2xcosx

18.

$f\left(x\right)\ =\ x^{4\ }\sin\ x$ Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

19.

Find the fully simplified Derivative of y = 4x² + 3x + 6x^-2

a)

y' = 8x + 3 -12x^-3

b)

y' = 8x + 3 +12/x³

c)

y' = 8x + 3 -12/x³

d)

y' = 8x + 3 + 12/x

20.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

21.

At which point(s) will the slopes of the tangent line be zero?

a)

at C only

b)

at points A, C and E only

c)

at point B and D only

d)

at points A and E only

22.

Find the slope of f(x) = -3x²- 6x at x = 1.

a)

m = 0

b)

f'(x) = -6x - 6

c)

f'(x) = 6x

d)

m = -12

23.

Differentiate f(x) = (2/x⁵) - 5.

a)

x⁵- 3

b)

-10x⁶

c)

x⁵- 5

d)

-10x^-6

24.

Find the derivative of y = 2x² (3x - 4)

a)

6x³ - 8x²

b)

18x² - 16x

c)

15x²- 6x

d)

6x - 4

25.

The derivative of

a)

y'=2x-x^-2

b)

y'=x^-1+8x

c)

y'=x^-2+8x

d)

y=8x-x^-2

26.

Find the slope of y = 3x² - 5 at x = 2

a)

10

b)

11

c)

12

d)

13

27.

Find the derivative.

y = x²/ (3x - 1)

a)

y' = 9x²- 12

y' = (3x - 1) / (3x - 1)²

b)

y' = (3x² - 2x) / (3x - 1)²

c)

y' = (6x + 1)²/ 3

28.

Differentiate y = $\frac{12}{x^2}$

a)

y' = 24x^-1

b)

y' = -24x^-3

c)

y' = -24x^-1

d)

y' = 6x^-3

29.

Differentiate y = $\frac{2x^2+x-3}{x}$

a)

y = 2x + 1 - 3x^-1

b)

y' = 4x + 1 - 1x^-2

c)

y' = 2 + 3x^-2

d)

y' = 4x + 1 - 3x^-2

30.

Find the derivative of g(x)=(3x-2)/(x²+2)

a)

9x²+2

b)

3(x²+2)/(x²+2)²

c)

(-3x²+4x +6)/(x²+2)²

d)

(-3x²+10)/(x²+2)²

31.

Differentiate (2x + 2)(x - 5)⁸ with respect to x.

a)

(2x + 2)(x - 5)⁷ + 2(x - 5)⁸

b)

8(2x + 2)(x - 5)⁷ + 2(x - 5)⁸

c)

2(x - 5)⁸

d)

16(x - 5)⁷

32.

What is the derivative of csc(x)?

a)

csc(x)cot(x)

b)

-csc(x)cot(x)

c)

-csc²(x)

d)

-cot²(x)

33.

Find the derivative of f(x) = x²sinx

a)

f'(x) = 2xsinx - x²cosx

b)

f'(x) = 2xsinx + x²sinx

c)

f'(x) = 2xsinx + x²cosx

d)

f'(x) = 2xcosx

34.

How many derivatives can you take of a function?

a)

only 3

b)

only 2

c)

only 1

d)

until you can no longer derive it

35.

secxtanx is the derivative of which function?

a)

tanx

b)

cotx

c)

secx

d)

cscx

36.

a)

4x²+8x+1

b)

20x⁶+5x⁴

c)

28x⁶+5x⁴-16x

37.

Find the derivative of f(x) = (x⁶ + 4)⁵

a)

f '(x) = 5x⁵(x⁴ + 4)⁴

b)

f '(x) = 6x⁵(x⁶ + 4)⁴

c)

f '(x) = 30x⁵(x⁶ + 4)⁴

d)

f '(x) = 30x⁶(x⁶ + 4)⁴

38.

Find the derivative of f(x)=(x³-2x)²

a)

6x⁵ - 12x³+8x

b)

6x⁵ - 16x³+8x

c)

x⁶-4x⁴+4x²

d)

6x⁵ - 16x^3-8x

39.

Find the derivative of f(x)=(x³-2x)²

a)

6x⁵ - 12x³+8x

b)

6x⁵ - 16x³+8x

c)

x⁶-4x⁴+4x²

d)

6x⁵ - 16x^3-8x

40.

find y' for y=(e^5x)+1

a)

5e^5x+1

b)

e^5x

c)

5e^5x

d)

1

41.

find y' for y= (2x+1)¹⁰

a)

10(2x+1)⁹

b)

20(2x-1)⁹

c)

20(2x+1)¹⁰

d)

20(2x+1)⁹

42.

find y' for y= sin(2x²)

a)

4sin(2x²)

b)

4xcos(2x²)

c)

2xcos(2x²)

d)

xcos(4x²)

43.

Differentiate:
f(x) = x⁷ (5 + 8x)³

a)

f '(x) = x² (5 + 8x)⁶ (35 + 80x)

b)

f '(x) = x⁶ (5 + 8x)² (35 + 80x)

c)

f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)

d)

f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

44.

$\frac{\text{d}}{\text{d}x}\left[\left(2x+1\right)\left(5x-4\right)\right]$

a)

$10x-3$

b)

$20x-4$

c)

$10x-4$

d)

$20x-3$

45.

$\frac{\text{d}}{\text{d}x}\left[\left(\sqrt{x}\right)\left(x-1\right)\right]$

a)

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

b)

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

c)

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

d)

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

46.

$\frac{\text{d}}{\text{d}x}\left[x^2\left(x+1\right)\left(2x-3\right)\right]$

a)

$8x^3-3x^2-6x$

b)

$8x^3+3x^2-6x$

c)

$8x^3-3x^2+6x$

d)

$8x^3+3x^2+6x$

47.

Find the derivative
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)

48.

Find the slope of f(x) = -3x²-6x at x = 1.

a)

m = 0

b)

f'(x) = -6x - 6

c)

f'(x) = 6x

d)

m = -12

49.

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

a)

cos(x)

b)

x sin(x)

c)

$\frac{1}{x}$

d)

$\sin^2\ \left(x\right)$

50.

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

a)

-sin(x)

b)

x sin(x)

c)

$\frac{1}{x}$

d)

$\sin^2\ \left(x\right)$

51.

$\frac{d}{dx}\arccos\left(x\right)$ =

a)

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

b)

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

c)

$\frac{1}{x}$

d)

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

52.

$\frac{d}{dx}\operatorname{arccot}\left(x\right)$ =

a)

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

b)

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

c)

$\frac{1}{x}$

d)

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

53.

$\frac{d}{dx}\arctan\left(x\right)$ =

a)

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

b)

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

c)

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

d)

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

54.

$\frac{d}{dx}\arcsin\left(x\right)$ =

a)

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

b)

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

c)

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

d)

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

55.

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

a)

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

b)

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

c)

$\frac{1}{x}$

d)

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

56.

$\frac{d}{dx}\ln\left(1-x\right)$ =

a)

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

b)

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

c)

$\frac{1}{x}$

d)

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

57.

$\frac{d}{dx}\left(x\ -\ \ln\left(1+x\right)\right)$ =

a)

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

b)

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

c)

$\frac{1}{x}$

d)

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

58.

$\frac{d}{dx}\sqrt{x^2+1}$ =

a)

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

b)

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

c)

$\frac{1}{x}$

d)

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

midterm calculus honors

Total questions: 58

Worksheet time: 58mins

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