Math 16A - Derivative Review
Directions
1. Use the definition of the derivative to compute f ′(x)
2. Use any rule(s) you know to compute the derivative of
the function
3. Use any rule(s) you know to compute the derivative of
the function
4. Use the product, quotient or chain rule (or combination) to take the derivative
5. Find the equation of the tangent line to the curve at
the indicated point
6. Create your own derivative problem that requires the
given rule(s) and solve it
1
Group 1
Group 2
1
5x
√
1
2. x − 5 + ex+3 − x
x
e6x − 2x3
3.
csc(−x)
√
4. tan(sec( x3 ))
√
5. 2x, x = 8
1. x2 + 2x + 4
1.
2. x44 − x3/4 + sin(3x) − 2
√
3. cot ( sin(e2x ))
(x2 − 1)2
x2 + 1
5. ex + x2 , x = 0
4.
6. Chain and Chain
6. Chain and Product
Group 3
√
1. x − 4
Group 4
1. x2 + 7x − 3
2. 3x4/3 + 5x8 − 2 tan(2x) + πx
√
6
2
2. csc(2x) − 6 3x + 7 − ex
x
3. (14x6 − 1)3 ⋅ sin(−x)
√
2
4. ex +2x+2 ⋅ cos( x)
x
5. tan ( ) ,
2
3. sec (x2 e4x )
x+1
)
x−1
5. x6 + x5 + 7x − 4,
4. cot (
π
x=
2
6. Product and Quotient
x=0
6. Chain and Quotient
2