What is the derivative of (x-2(x+1)(x+5)) ?

The derivative of (x-2(x+1)(x+5)) is 3x^2+8x-7

What is the first derivative of (x-2(x+1)(x+5)) ?

The first derivative of (x-2(x+1)(x+5)) is 3x^2+8x-7

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\frac{d}{d x} ((x - 2) (x + 1) (x + 5))

3 x^{2} + 8 x - 7

Solution steps

\frac{d}{d x} ((x - 2) (x + 1) (x + 5))

Apply the Product Rule:

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

f = x - 2, g = (x + 1) (x + 5)

= \frac{d}{d x} (x - 2) (x + 1) (x + 5) + \frac{d}{d x} ((x + 1) (x + 5)) (x - 2)

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

\frac{d}{d x} ((x + 1) (x + 5)) = 2 x + 6

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

Simplify

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

= 3 x^{2} + 8 x - 7

\int (x^{2} - 4 x - 15) d x

\int x^{2} cos (4 x) d x

\int x + y d x

f (x) = sin (8 e^{x})

\int (3 x^{2} y) d x

What is the derivative of (x-2(x+1)(x+5)) ?
The derivative of (x-2(x+1)(x+5)) is 3x^2+8x-7
What is the first derivative of (x-2(x+1)(x+5)) ?
The first derivative of (x-2(x+1)(x+5)) is 3x^2+8x-7