Basic Derivatives
Product and Quotient Rule
Chain Rule
Implicit Differentiation
100
What is the derivative of y = 3x
2
?
y' = 6x
100
Find the derivative of y = 3x
2
sin x
3x
2
cos x + 6x sin x
100
Find y' if y = (3x - 9)
4
12(3x - 9)
3
100
Find the derivative implicitly x
2
+ y
2
= 30
y' = - x/y
200
Find the derivative of f(x) = 5
0
200
f(x) = (3x - 2x
2
)(5 + 4x)
-24x
2
+ 4x + 15
200
Find the derivative of f(x) = sin 4x
4 cos 4x
200
sin x + 2cos 2y = 1
y' = cosx/4sin2y
300
Find the derivative of f(x) = 6x
3
+ x - 2
18x
2
+ 1
300
Find the derivative of y = (5x - 2)/(x
2
+ 1)
(-5x
2
+ 4x + 5)/(x
2
+ 1)
2
300
Find y' if y = (9x
2
+ 4)
1/3
(6x)/(9x
2
+ 4)
2/3
300
(y - 2)
2
= 4x - 12
y' = 2/(y - 2)
400
Find the derivative of f(x) = 3sinx - 2cosx
3cosx + 2sinx
400
Find the derivative of f(x) = (2x + 5)/(x)
1/2
(2x - 5)/(2x
3/2
)
400
f(x) = sin
3
4x Find f'(x)
12sin
2
4x cos 4x
400
x
3
- 3x
2
y + 2xy
2
= 12
y' = (-3x
2
+ 6xy - 2y
2
)/(-3x
2
+ 4xy)
Continue
ESC
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