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Popular >

derivative of (x-5)(x+4)(x+6)

Solution

derivative of

(x - 5) (x + 4) (x + 6)

Solution

3 x^{2} + 10 x - 26

Solution steps

\frac{d}{d x} ((x - 5) (x + 4) (x + 6))

Apply the Product Rule:

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

f = x - 5, g = (x + 4) (x + 6)

= \frac{d}{d x} (x - 5) (x + 4) (x + 6) + \frac{d}{d x} ((x + 4) (x + 6)) (x - 5)

\frac{d}{d x} (x - 5) = 1

\frac{d}{d x} ((x + 4) (x + 6)) = 2 x + 10

= 1 \cdot (x + 4) (x + 6) + (2 x + 10) (x - 5)

Simplify

1 \cdot (x + 4) (x + 6) + (2 x + 10) (x - 5) : 3 x^{2} + 10 x - 26

= 3 x^{2} + 10 x - 26

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Frequently Asked Questions (FAQ)

What is the derivative of (x-5)(x+4)(x+6) ?
The derivative of (x-5)(x+4)(x+6) is 3x^2+10x-26
What is the first derivative of (x-5)(x+4)(x+6) ?
The first derivative of (x-5)(x+4)(x+6) is 3x^2+10x-26