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) = 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

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

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

Success!

ƒ⁽⁴⁾(0) = 0

↓Steps Explained:↓

Final Answer

ƒ⁽⁴⁾(0) = 0

Related Calculators: Polynomial | Monomials | Synthetic Division

ƒ()
ƒ'()

n =

Enter your expression below:

Start ƒ'(h)

Use the power rule

Collecting all of our derivative terms

Start ƒ''(h)

Use the power rule

Collecting all of our derivative terms

Start ƒ(3)(h)

Use the power rule

Collecting all of our derivative terms

Start ƒ(4)(h)

Collecting all of our derivative terms

Evaluate ƒ(4)(0)

Answer

↓Steps Explained:↓

Final Answer

Start ƒ⁽³⁾(h)

Start ƒ⁽⁴⁾(h)

Evaluate ƒ⁽⁴⁾(0)