What is the derivative of 5(x^2+2x)^3 ?

The derivative of 5(x^2+2x)^3 is 15(x^2+2x)^2(2x+2)

What is the first derivative of 5(x^2+2x)^3 ?

The first derivative of 5(x^2+2x)^3 is 15(x^2+2x)^2(2x+2)

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derivative of

5 (x^{2} + 2 x)^{3}

15 (x^{2} + 2 x)^{2} (2 x + 2)

Solution steps

\frac{d}{d x} (5 (x^{2} + 2 x)^{3})

Take the constant out:

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

= 5 \frac{d}{d x} ((x^{2} + 2 x)^{3})

Apply the chain rule:

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

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

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

= 5 \cdot 3 (x^{2} + 2 x)^{2} (2 x + 2)

Simplify

= 15 (x^{2} + 2 x)^{2} (2 x + 2)

x e^{x^{2}} (x^{2} + 1)^{8}

\int \frac{y}{3 y + 5} d y

\int e^{- 2 x} 2 x d x

(4 x)^{2 x}

n = 0 \sum \infty \frac{1}{n ^{1.1}}

What is the derivative of 5(x^2+2x)^3 ?
The derivative of 5(x^2+2x)^3 is 15(x^2+2x)^2(2x+2)
What is the first derivative of 5(x^2+2x)^3 ?
The first derivative of 5(x^2+2x)^3 is 15(x^2+2x)^2(2x+2)