What is the derivative of (3-x(2-x)(5-x)) ?

The derivative of (3-x(2-x)(5-x)) is -3x^2+20x-31

What is the first derivative of (3-x(2-x)(5-x)) ?

The first derivative of (3-x(2-x)(5-x)) is -3x^2+20x-31

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

- 3 x^{2} + 20 x - 31

Solution steps

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

Apply the Product Rule:

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

f = 3 - x, g = (2 - x) (5 - x)

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

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

\frac{d}{d x} ((2 - x) (5 - x)) = 2 x - 7

= (- 1) (2 - x) (5 - x) + (2 x - 7) (3 - x)

Simplify

(- 1) (2 - x) (5 - x) + (2 x - 7) (3 - x) : - 3 x^{2} + 20 x - 31

= - 3 x^{2} + 20 x - 31

\int (3 x - 2) e^{x} d x

\int (x + 3)^{3} d x

\int 2 x (x^{2} + 2)^{2} d x

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

f (x) = x sin (x) + cos (x)

What is the derivative of (3-x(2-x)(5-x)) ?
The derivative of (3-x(2-x)(5-x)) is -3x^2+20x-31
What is the first derivative of (3-x(2-x)(5-x)) ?
The first derivative of (3-x(2-x)(5-x)) is -3x^2+20x-31