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Popular >

derivative of (x+5(x-1)(x-7))

Solution

\frac{d}{d x} ((x + 5) (x - 1) (x - 7))

Solution

3 x^{2} - 6 x - 33

Solution steps

\frac{d}{d x} ((x + 5) (x - 1) (x - 7))

Apply the Product Rule:

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

f = x + 5, g = (x - 1) (x - 7)

= \frac{d}{d x} (x + 5) (x - 1) (x - 7) + \frac{d}{d x} ((x - 1) (x - 7)) (x + 5)

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

\frac{d}{d x} ((x - 1) (x - 7)) = 2 x - 8

= 1 \cdot (x - 1) (x - 7) + (2 x - 8) (x + 5)

Simplify

1 \cdot (x - 1) (x - 7) + (2 x - 8) (x + 5) : 3 x^{2} - 6 x - 33

= 3 x^{2} - 6 x - 33

Popular Examples

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\int sin^{5} (x co) s^{6} x d x

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f (x) = \frac{x ^{3} - 7 x ^{2} + 7}{x ^{2}}

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\frac{\partial}{\partial x} (y^{6} sin (2 x))

limit as x approaches infinity of-3x

x \to \infty lim (- 3 x)

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\frac{d}{d x} (a + \frac{1}{x})

Frequently Asked Questions (FAQ)

What is the derivative of (x+5(x-1)(x-7)) ?
The derivative of (x+5(x-1)(x-7)) is 3x^2-6x-33
What is the first derivative of (x+5(x-1)(x-7)) ?
The first derivative of (x+5(x-1)(x-7)) is 3x^2-6x-33