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Popular >

derivative of x(2x+1^3)

Solution

\frac{d}{d x} (x (2 x + 1)^{3})

Solution

(2 x + 1)^{3} + 6 x (2 x + 1)^{2}

Solution steps

\frac{d}{d x} (x (2 x + 1)^{3})

Apply the Product Rule:

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

f = x, g = (2 x + 1)^{3}

= \frac{d x}{d x} (2 x + 1)^{3} + \frac{d}{d x} ((2 x + 1)^{3}) x

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

\frac{d}{d x} ((2 x + 1)^{3}) = 6 (2 x + 1)^{2}

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

Simplify

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

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Frequently Asked Questions (FAQ)

What is the derivative of x(2x+1^3) ?
The derivative of x(2x+1^3) is (2x+1)^3+6x(2x+1)^2
What is the first derivative of x(2x+1^3) ?
The first derivative of x(2x+1^3) is (2x+1)^3+6x(2x+1)^2