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Popular >

derivative of x(2x+1)^3

Solution

derivative of

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}

Popular Examples

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(\partial)/(\partial x)(sqrt(x^2+4xy+y^6))

\frac{\partial}{\partial x} (x^{2} + 4 x y + y^{6})

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

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