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Popular >

derivative of x^2(x-12^2)

Solution

\frac{d}{d x} (x^{2} (x - 12)^{2})

Solution

4 x^{3} - 72 x^{2} + 288 x

Solution steps

\frac{d}{d x} (x^{2} (x - 12)^{2})

Apply the Product Rule:

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

f = x^{2}, g = (x - 12)^{2}

= \frac{d}{d x} (x^{2}) (x - 12)^{2} + \frac{d}{d x} ((x - 12)^{2}) x^{2}

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

\frac{d}{d x} ((x - 12)^{2}) = 2 (x - 12)

= 2 x (x - 12)^{2} + 2 (x - 12) x^{2}

Simplify

2 x (x - 12)^{2} + 2 (x - 12) x^{2} : 4 x^{3} - 72 x^{2} + 288 x

= 4 x^{3} - 72 x^{2} + 288 x

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Frequently Asked Questions (FAQ)

What is the derivative of x^2(x-12^2) ?
The derivative of x^2(x-12^2) is 4x^3-72x^2+288x
What is the first derivative of x^2(x-12^2) ?
The first derivative of x^2(x-12^2) is 4x^3-72x^2+288x