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Popular >

derivative of x^2(3x-4^3)

Solution

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

Solution

2 x (3 x - 4)^{3} + 9 (3 x - 4)^{2} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((3 x - 4)^{3}) = 9 (3 x - 4)^{2}

= 2 x (3 x - 4)^{3} + 9 (3 x - 4)^{2} x^{2}

Popular Examples

integral from 0 to 1 of x^2e^x

\int_{0}^{1} x^{2} e^{x} d x

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y = \frac{16}{x ^{2} - 6 x - 55}, y = 0, x = - 3, x = 3

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Frequently Asked Questions (FAQ)

What is the derivative of x^2(3x-4^3) ?
The derivative of x^2(3x-4^3) is 2x(3x-4)^3+9(3x-4)^2x^2
What is the first derivative of x^2(3x-4^3) ?
The first derivative of x^2(3x-4^3) is 2x(3x-4)^3+9(3x-4)^2x^2