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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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Frequently Asked Questions (FAQ)

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