Given ƒ(h) = 9h

^{3}Determine the derivative ƒ'(h)

### Start ƒ'(h)

## Use the power rule

ƒ'(h) of ah

^{n} = (a * n)h

^{(n - 1)}For this term, a = 9, n = 3

and h is the variable we derive

ƒ'(h) = 9h

^{3}ƒ'(h)( = 9 * 3)h

^{(3 - 1)}ƒ'(h) = 27h

^{2}

## Collecting all of our derivative terms

ƒ'(h) =

**27h**^{2}### Start ƒ''(h)

## Use the power rule

ƒ''(h) of ah

^{n} = (a * n)h

^{(n - 1)}For this term, a = 27, n = 2

and h is the variable we derive

ƒ''(h) = 27h

^{2}ƒ''(h)( = 27 * 2)h

^{(2 - 1)}ƒ''(h) = 54h

## Collecting all of our derivative terms

ƒ''(h) =

**54h**### Start ƒ^{(3)}(h)

## Use the power rule

ƒ

^{(3)}(h) of ah

^{n} = (a * n)h

^{(n - 1)}For this term, a = 54, n = 1

and h is the variable we derive

ƒ

^{(3)}(h) = 54h

ƒ

^{(3)}(h)( = 54 * 1)h

^{(1 - 1)}ƒ

^{(3)}(h) = 54

## Collecting all of our derivative terms

ƒ

^{(3)}(h) =

**54**### Start ƒ^{(4)}(h)

## Collecting all of our derivative terms

ƒ

^{(4)}(h) =

## Evaluate ƒ^{(4)}(0)

ƒ

^{(4)}(0) =

ƒ

^{(4)}(0) =

ƒ

^{(4)}(0) =

##### Final Answer

ƒ^{(4)}(0) = **0**

##### How does the Functions-Derivatives-Integrals Calculator work?

Free Functions-Derivatives-Integrals Calculator - Given a polynomial expression, this calculator evaluates the following items:

1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1^{st} Derivative ƒ‘(x) The derivative of your expression will also be evaluated at a point, i.e., ƒ‘(1)

3) 2^{nd} Derivative ƒ‘‘(x) The second derivative of your expression will be also evaluated at a point, i.e., ƒ‘‘(1)

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

This calculator has 7 inputs.

### What 1 formula is used for the Functions-Derivatives-Integrals Calculator?

Power Rule:
f(x) = x

^{n}, f‘(x) = nx

^{(n - 1)}For more math formulas, check out our

Formula Dossier
### What 8 concepts are covered in the Functions-Derivatives-Integrals Calculator?

- derivative
- rate at which the value y of the function changes with respect to the change of the variable x
- exponent
- The power to raise a number
- function
- relation between a set of inputs and permissible outputs

ƒ(x) - functions-derivatives-integrals
- integral
- a mathematical object that can be interpreted as an area or a generalization of area
- point
- an exact location in the space, and has no length, width, or thickness
- polynomial
- an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
- power
- how many times to use the number in a multiplication

##### Example calculations for the Functions-Derivatives-Integrals Calculator

## Tags:

Add This Calculator To Your Website