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

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

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

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

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derivative of

f (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

x \to 4 + lim (3 x - 5)

\frac{d v}{d t} = 4 e^{3 t - 4 v}

x \to 0 lim (2 x ln (x))

\int 3 cos (4 x - 1) d x

\int - \frac{3 ( x - 6 )}{x ^{2} - 17 x + 72} d x

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