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Popular >

derivative of x(17-2x(33-2x))

Solution

\frac{d}{d x} (x (17 - 2 x) (33 - 2 x))

Solution

12 x^{2} - 200 x + 561

Solution steps

\frac{d}{d x} (x (17 - 2 x) (33 - 2 x))

Apply the Product Rule:

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

f = x, g = (17 - 2 x) (33 - 2 x)

= \frac{d x}{d x} (17 - 2 x) (33 - 2 x) + \frac{d}{d x} ((17 - 2 x) (33 - 2 x)) x

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

\frac{d}{d x} ((17 - 2 x) (33 - 2 x)) = 8 x - 100

= 1 \cdot (17 - 2 x) (33 - 2 x) + (8 x - 100) x

Simplify

1 \cdot (17 - 2 x) (33 - 2 x) + (8 x - 100) x : 12 x^{2} - 200 x + 561

= 12 x^{2} - 200 x + 561

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Frequently Asked Questions (FAQ)

What is the derivative of x(17-2x(33-2x)) ?
The derivative of x(17-2x(33-2x)) is 12x^2-200x+561
What is the first derivative of x(17-2x(33-2x)) ?
The first derivative of x(17-2x(33-2x)) is 12x^2-200x+561