What is the derivative of (x^2+x(6-x)) ?

The derivative of (x^2+x(6-x)) is -3x^2+10x+6

What is the first derivative of (x^2+x(6-x)) ?

The first derivative of (x^2+x(6-x)) is -3x^2+10x+6

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\frac{d}{d x} ((x^{2} + x) (6 - x))

- 3 x^{2} + 10 x + 6

Solution steps

\frac{d}{d x} ((x^{2} + x) (6 - x))

Apply the Product Rule:

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

f = x^{2} + x, g = 6 - x

= \frac{d}{d x} (x^{2} + x) (6 - x) + \frac{d}{d x} (6 - x) (x^{2} + x)

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

\frac{d}{d x} (6 - x) = - 1

= (2 x + 1) (6 - x) + (- 1) (x^{2} + x)

Simplify

(2 x + 1) (6 - x) + (- 1) (x^{2} + x) : - 3 x^{2} + 10 x + 6

= - 3 x^{2} + 10 x + 6

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