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Popular >

derivative of (x-3(x+6)(x-9))

Solution

\frac{d}{d x} ((x - 3) (x + 6) (x - 9))

Solution

3 x^{2} - 12 x - 45

Solution steps

\frac{d}{d x} ((x - 3) (x + 6) (x - 9))

Apply the Product Rule:

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

f = x - 3, g = (x + 6) (x - 9)

= \frac{d}{d x} (x - 3) (x + 6) (x - 9) + \frac{d}{d x} ((x + 6) (x - 9)) (x - 3)

\frac{d}{d x} (x - 3) = 1

\frac{d}{d x} ((x + 6) (x - 9)) = 2 x - 3

= 1 \cdot (x + 6) (x - 9) + (2 x - 3) (x - 3)

Simplify

1 \cdot (x + 6) (x - 9) + (2 x - 3) (x - 3) : 3 x^{2} - 12 x - 45

= 3 x^{2} - 12 x - 45

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (x-3(x+6)(x-9)) ?
The derivative of (x-3(x+6)(x-9)) is 3x^2-12x-45
What is the first derivative of (x-3(x+6)(x-9)) ?
The first derivative of (x-3(x+6)(x-9)) is 3x^2-12x-45