04 - Derivative at a Value PDF

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Kuta Software - Infinite Calculus

Name___________________________________

Derivative at a Value

Date________________ Period____

For each problem, find the derivative of the function at the given value. 1) y = x 2 + 4 x at x = −5

3) y =

2) y = −x 3 + 4x 2 − 4 at x = 4

20 at x = 3 x +5

4) y =

2

1

5) y = ( −x + 4)

2

2 at x = 5 x+1

1

6) y = (−3 x + 9) 2 at x = −5

at x = 0

8) y = − ln ( x + 3) at x = 5

7) y = e −x + 2 at x = 4

9) y = 2sin (2x) at x = −

π 2

10) y = −tan (2x) at x = −π

Kuta Software - Infinite Calculus

Name___________________________________

Derivative at a Value

Date________________ Period____

For each problem, find the derivative of the function at the given value. 1) y = x 2 + 4 x at x = −5 dy dx

2) y = −x 3 + 4x 2 − 4 at x = 4 dy dx

= −6 x = −5

3) y =

x=4

20 at x = 3 x +5

4) y =

2

dy

=−

dx

2 at x = 5 x+1

30

dy

49

dx

x=3

5)

= −16

1

=−

18 x=5

1

1

y = (−x + 4) 2

y = (−3 x + 9) 2

dy dx

=−

at x = 0

6)

1 4

=−

dx

8

8) y = − ln ( x + 3) at x = 5 dy dx

1 e2

9) y = 2sin (2x) at x = − dy dx

= −4

=−

1 8

x=5

x=4

x=−

=− x = −5

7) y = e −x + 2 at x = 4 dy

6

dy dx

x=0

at x = −5

π 2

10) y = −tan (2x) at x = −π dy dx

= −2 x = −π

π 2

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