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Popular >

derivative of x(x-15^2)

Solution

\frac{d}{d x} (x (x - 15)^{2})

Solution

3 x^{2} - 60 x + 225

Solution steps

\frac{d}{d x} (x (x - 15)^{2})

Apply the Product Rule:

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

f = x, g = (x - 15)^{2}

= \frac{d x}{d x} (x - 15)^{2} + \frac{d}{d x} ((x - 15)^{2}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((x - 15)^{2}) = 2 (x - 15)

= 1 \cdot (x - 15)^{2} + 2 (x - 15) x

Simplify

1 \cdot (x - 15)^{2} + 2 (x - 15) x : 3 x^{2} - 60 x + 225

= 3 x^{2} - 60 x + 225

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Frequently Asked Questions (FAQ)

What is the derivative of x(x-15^2) ?
The derivative of x(x-15^2) is 3x^2-60x+225
What is the first derivative of x(x-15^2) ?
The first derivative of x(x-15^2) is 3x^2-60x+225