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Popular >

derivative of x(3x+4)^2

Solution

derivative of

x (3 x + 4)^{2}

Solution

27 x^{2} + 48 x + 16

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((3 x + 4)^{2}) = 6 (3 x + 4)

= 1 \cdot (3 x + 4)^{2} + 6 (3 x + 4) x

Simplify

1 \cdot (3 x + 4)^{2} + 6 (3 x + 4) x : 27 x^{2} + 48 x + 16

= 27 x^{2} + 48 x + 16

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Frequently Asked Questions (FAQ)

What is the derivative of x(3x+4)^2 ?
The derivative of x(3x+4)^2 is 27x^2+48x+16
What is the first derivative of x(3x+4)^2 ?
The first derivative of x(3x+4)^2 is 27x^2+48x+16