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Popular >

derivative of P(x)=x(x-8)(x+5)

Solution

derivative of

P (x) = x (x - 8) (x + 5)

Solution

3 x^{2} - 6 x - 40

Solution steps

\frac{d}{d x} (x (x - 8) (x + 5))

Apply the Product Rule:

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

f = x, g = (x - 8) (x + 5)

= \frac{d x}{d x} (x - 8) (x + 5) + \frac{d}{d x} ((x - 8) (x + 5)) x

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

\frac{d}{d x} ((x - 8) (x + 5)) = 2 x - 3

= 1 \cdot (x - 8) (x + 5) + (2 x - 3) x

Simplify

1 \cdot (x - 8) (x + 5) + (2 x - 3) x : 3 x^{2} - 6 x - 40

= 3 x^{2} - 6 x - 40

Popular Examples

integral from 0 to 2 of (x/((3-x)^2))

\int_{0}^{2} (\frac{x}{( 3 - x ) ^{2}}) d x

y^{^{'}} = 3 y + x e^{x}

integral of 2arctan(y/x)

\int 2 arctan (\frac{y}{x}) d x

integral of (x^3+3x^2+5x+4)/(x^2+3x+2)

\int \frac{x ^{3} + 3 x ^{2} + 5 x + 4}{x ^{2} + 3 x + 2} d x

integral of 90x^8(1-x)

\int 90 x^{8} (1 - x) d x

Frequently Asked Questions (FAQ)

What is the derivative of P(x)=x(x-8)(x+5) ?
The derivative of P(x)=x(x-8)(x+5) is 3x^2-6x-40
What is the first derivative of P(x)=x(x-8)(x+5) ?
The first derivative of P(x)=x(x-8)(x+5) is 3x^2-6x-40