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Popular >

derivative of x^3(2x+1^3)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Graph

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Frequently Asked Questions (FAQ)

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