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1. Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified.

G(t)= 9/t^2; g ‘(4), g ‘(sqrt5)

g ‘(t)= ?

g ‘(-4)= ? (type the integer or simplified fraction.)

g ‘(4)=?

g ‘(sqrt5)=?

2. find the first and second derivatives

y=6x^-3- 5/x ← that is 5 over x

dy/dx=?

d^2y/dx^2=?

3. find the derivative of the function.

y= 9x-1 / 3x+5

the derivative is y’=?

4. find dy / dx for y= csc x / 1+ csc x

dy/dx=?

5. find dp / dq for p= sin q + cos q / cos q

dp/dq=?

6. write the function in the form y=f(u) and u= g(x). Then find dy / dx as a function of x.

y=(-8 - 5x /8) ^-8

u=? (type an expression using x as the variable)

y=? (type an expression using u as the variable)

dy/dx=? (type an expression using x as the variable)

7. write the function in the form y=f(u) and u= g(x). Then find dy / dx as a function of x.

y= e ^7-3x

what is the correct form of y in terms u?

dy / dx=?

8. find the derivative of the given function.

y= (x^2 -8x + 8) e ^9x/8

dy / dx=?

9. use implicit differentiation to find dy / dx.

5y^2= 3x-4 / 3x+4

dy / dx=?

10. find dy / dx

e ^5x= sin (x+7y)

dy / dx=?

11. let f(x)= 3x^3 – 5x^2 – 4, x> or =1.5. Find the values of df^-1 / dx at the point x=108=f(4).

The value of df^-1 / dx at the point x= 108= f(4) is? (type the simplified fraction)

12. Find the derivative of y with the respect to x of y= ln(13x) / 13x.

The derivative of y with respect to x of y= ln(13x) / 13x is?

13. Find the exact value, in radians, of the expression cot^-1 (sqrt3 / 3) =?

14. Find the exact value of the following with out using a calculator.

sin(sin^-1(1 / 4) + tan^-1 (-4))=? (Simplify your answer. type an exact answer, using radicals as needed. Rationalize all dominators.)

G(t)= 9/t^2; g ‘(4), g ‘(sqrt5)

g ‘(t)= ?

g ‘(-4)= ? (type the integer or simplified fraction.)

g ‘(4)=?

g ‘(sqrt5)=?

2. find the first and second derivatives

y=6x^-3- 5/x ← that is 5 over x

dy/dx=?

d^2y/dx^2=?

3. find the derivative of the function.

y= 9x-1 / 3x+5

the derivative is y’=?

4. find dy / dx for y= csc x / 1+ csc x

dy/dx=?

5. find dp / dq for p= sin q + cos q / cos q

dp/dq=?

6. write the function in the form y=f(u) and u= g(x). Then find dy / dx as a function of x.

y=(-8 - 5x /8) ^-8

u=? (type an expression using x as the variable)

y=? (type an expression using u as the variable)

dy/dx=? (type an expression using x as the variable)

7. write the function in the form y=f(u) and u= g(x). Then find dy / dx as a function of x.

y= e ^7-3x

what is the correct form of y in terms u?

dy / dx=?

8. find the derivative of the given function.

y= (x^2 -8x + 8) e ^9x/8

dy / dx=?

9. use implicit differentiation to find dy / dx.

5y^2= 3x-4 / 3x+4

dy / dx=?

10. find dy / dx

e ^5x= sin (x+7y)

dy / dx=?

11. let f(x)= 3x^3 – 5x^2 – 4, x> or =1.5. Find the values of df^-1 / dx at the point x=108=f(4).

The value of df^-1 / dx at the point x= 108= f(4) is? (type the simplified fraction)

12. Find the derivative of y with the respect to x of y= ln(13x) / 13x.

The derivative of y with respect to x of y= ln(13x) / 13x is?

13. Find the exact value, in radians, of the expression cot^-1 (sqrt3 / 3) =?

14. Find the exact value of the following with out using a calculator.

sin(sin^-1(1 / 4) + tan^-1 (-4))=? (Simplify your answer. type an exact answer, using radicals as needed. Rationalize all dominators.)

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