Given ƒ(h) = 9h3
Determine the derivative ƒ'(h)
Start ƒ'(h)
Use the power rule
ƒ'(h) of ahn = (a * n)h(n - 1)For this term, a = 9, n = 3
and h is the variable we derive
ƒ'(h) = 9h3
ƒ'(h)( = 9 * 3)h(3 - 1)
ƒ'(h) = 27h2
Collecting all of our derivative terms
ƒ'(h) = 27h2Start ƒ''(h)
Use the power rule
ƒ''(h) of ahn = (a * n)h(n - 1)For this term, a = 27, n = 2
and h is the variable we derive
ƒ''(h) = 27h2
ƒ''(h)( = 27 * 2)h(2 - 1)
ƒ''(h) = 54h
Collecting all of our derivative terms
ƒ''(h) = 54hStart ƒ(3)(h)
Use the power rule
ƒ(3)(h) of ahn = (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) = 54Start 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
What is the 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) 1st Derivative ƒ‘(x) The derivative of your expression will also be evaluated at a point, i.e., ƒ‘(1)
3) 2nd 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.
1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)
2) 1st Derivative ƒ‘(x) The derivative of your expression will also be evaluated at a point, i.e., ƒ‘(1)
3) 2nd 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) = xn, f‘(x) = nx(n - 1)
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
