Enter your expression below:

ƒ()
ƒ'()
n =

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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

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Collecting all of our derivative terms

ƒ'(h) = 27h²

Start 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

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Collecting all of our derivative terms

ƒ''(h) = 54h

Start 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

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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) =

Answer

↓Steps Explained:↓

Final Answer

ƒ⁽⁴⁾(0) = 0

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