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Popular >

derivative of x(30-2x)^2

Solution

derivative of

x (30 - 2 x)^{2}

Solution

12 x^{2} - 240 x + 900

Solution steps

\frac{d}{d x} (x (30 - 2 x)^{2})

Apply the Product Rule:

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

f = x, g = (30 - 2 x)^{2}

= \frac{d x}{d x} (30 - 2 x)^{2} + \frac{d}{d x} ((30 - 2 x)^{2}) x

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

\frac{d}{d x} ((30 - 2 x)^{2}) = - 4 (30 - 2 x)

= 1 \cdot (30 - 2 x)^{2} + (- 4 (30 - 2 x)) x

Simplify

1 \cdot (30 - 2 x)^{2} + (- 4 (30 - 2 x)) x : 12 x^{2} - 240 x + 900

= 12 x^{2} - 240 x + 900

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Frequently Asked Questions (FAQ)

What is the derivative of x(30-2x)^2 ?
The derivative of x(30-2x)^2 is 12x^2-240x+900
What is the first derivative of x(30-2x)^2 ?
The first derivative of x(30-2x)^2 is 12x^2-240x+900