What is the derivative of f(x)=4(x^2+4x)^3 ?

The derivative of f(x)=4(x^2+4x)^3 is 12(x^2+4x)^2(2x+4)

What is the first derivative of f(x)=4(x^2+4x)^3 ?

The first derivative of f(x)=4(x^2+4x)^3 is 12(x^2+4x)^2(2x+4)

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derivative of

f (x) = 4 (x^{2} + 4 x)^{3}

12 (x^{2} + 4 x)^{2} (2 x + 4)

Solution steps

\frac{d}{d x} (4 (x^{2} + 4 x)^{3})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} ((x^{2} + 4 x)^{3})

Apply the chain rule:

3 (x^{2} + 4 x)^{2} \frac{d}{d x} (x^{2} + 4 x)

= 3 (x^{2} + 4 x)^{2} \frac{d}{d x} (x^{2} + 4 x)

\frac{d}{d x} (x^{2} + 4 x) = 2 x + 4

= 4 \cdot 3 (x^{2} + 4 x)^{2} (2 x + 4)

Simplify

= 12 (x^{2} + 4 x)^{2} (2 x + 4)

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What is the derivative of f(x)=4(x^2+4x)^3 ?
The derivative of f(x)=4(x^2+4x)^3 is 12(x^2+4x)^2(2x+4)
What is the first derivative of f(x)=4(x^2+4x)^3 ?
The first derivative of f(x)=4(x^2+4x)^3 is 12(x^2+4x)^2(2x+4)