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WorksheetsDerivatives
Total questions: 15
Worksheet time: 1hrs 15mins
Name
Class
Date
1.
Find the derivative of the given equation
f(x) = x4 + 4x3 - 2x2
f(x) = x4 + 4x3 - 2x2
a)
x3 + x2 - x
b)
4x3 + 12x2 + 4x
c)
4x + 12x - 4x
d)
4x3 + 12x2 - 4x
2.
Find the derivative of f(x) = 5x2 + 7x - 3.
a)
2x + 7
b)
10x + 7
c)
10x + 4
d)
2x + 4
3.
Find the slope of the tangent line to f(x) = -3x2-6x at x = 1.
a)
m = 0
b)
f'(x) = -6x - 6
c)
f'(x) = 6x
d)
m = -12
4.
If f(x)=(6x2-5x)7
what is f'(x)?
what is f'(x)?
a)
7(6x2-5x)6
b)
7(6x2-5x)6⋅(12x)
c)
7(6x2-5x)6⋅(12x-5)
d)
(12x-5)
5.
Find the derivative of this function
a)
(8x3 -60x/(2x2-5)2
b)
16x4/(2x2-5)2
c)
(8x4 -60x2)/(2x2-5)2
d)
3x/(2x2-5)2
6.
What is the equation of the tangent to the curve f(x)= 4x2+2x-1 at the point x=0?
a)
y+1=2(x+1)
b)
y = 2x - 1
c)
y=2x+2
d)
y = 2x -3
7.
Determine the derivative of: f(x) = x4sinx
a)
x4 cosx - 4x3sinx
b)
x4 cosx + 4x3sinx
c)
4x3cosx
d)
-4x3cosx
8.
Find the derivative f(x) = tanxcosx
a)
f'(x) = sec2xcosx - tanxsinx
b)
f'(x) = sec2xcosx + tanxsinx
c)
f'(x) = sec2xsinx
d)
f'(x) = sec2xcosx - tanxcosx
9.
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)
10.
Find the derivative of f(x) = -3x4cscx
a)
f'(x) = 12x3cscxcotx
b)
f'(x) = -3x4cscxcotx
c)
f'(x) =-12x3cscx + 3x4cotxcscx
d)
f'(x) = -3xcosx
11.
Find dy/dx by Implicit Differentiation
x3 +y3 = 36
x3 +y3 = 36
a)
6 -x
b)
3x2 +3y2
c)
−x2/y2
d)
0
12.
Find dy/dx by Implicit Differentiation
2xy3 - x2y = 2
2xy3 - x2y = 2
a)
2xy - 2y3
b)
2y(x-y2)/x(6y2-x)
c)
-2y/x
d)
2
13.
find y' for y= sin(2x2)
a)
4sin(2x2)
b)
4xcos(2x2)
c)
2xcos(2x2)
d)
xcos(4x2)
14.
Find the second derivative of the function:
f (x) = sin (5x6)
f (x) = sin (5x6)
a)
f ''(x) = 30x4 cos 5x6 + 30x10 sin 5x6
b)
f ''(x) = 180x4 cos 5x6 - 900x10 sin 5x6
c)
f ''(x) = 150x4 cos 5x6 + 900x10 sin 5x6
d)
f ''(x) = 150x4 cos 5x6 - 900x10 sin 5x6
15.
What is the derivative of area with respect to time?
a)
dtdA=2πr⋅dtdr
b)
dtdA=2πr
c)
dtdA=πr⋅dtdr
d)
dtdA=πr2⋅dtdr
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