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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

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\frac{\partial}{\partial x} (2 x + 3 y)

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x \to \infty lim (\frac{3}{3})

derivative of x^{ln(5})

\frac{d}{d x} (x^{l n (5)})

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n = 0 \sum \infty \frac{1}{n ^{2} + 5 n + 6}

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\int (5 x^{2} + 6 + \frac{9}{x ^{2} + 1}) d x

Frequently Asked Questions (FAQ)

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