1. Calculus Drill
Change each function to be
written in terms of y. Then
take the derivative.
1. ƒ (x) = x2 +5x – 9
2. ƒ(x) = x2√2x+1
3. ƒ(x) = (2x2 + 3x)3

2. Find the derivative!
1. ƒ(x) = √x(√3 x + √5
x)

3. Find the derivative!
x
4
3. ƒ(x) =( )x + 1

4. Find the Equation of the
tangent to the graph at
x = 3
1
√x2+7
3.ƒ(x) =

5. Calculus Objective
STW take
derivatives implicitly

6. Derivatives of Y
The derivative of y is
y’ or dy/dx.
Everything else you
do the same.

7. Examples
1. x + y = 10
Derivative 1 + y’ = 0
Solve for y’
y’ = –1

8. Examples
2. 2x2 + y2 = 5
Der. 4x + 2yy’ = 0
Solve for y’
y’ = – 2x/y

9. Examples
3. xy = 5
Derivative use the
product rule
u = x v= y
u’ = 1 v’ = y’

10. Examples
u = x v= y
u’ = 1 v’ = y’
Der. xy’ + y = 0
Solve for y’
–y/x = y’