What is (\partial)/(\partial x)((90-x)^2*(x+2)) ?

The answer to (\partial)/(\partial x)((90-x)^2*(x+2)) is 3x^2-356x+7740

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(\partial)/(\partial x)((90-x)^2*(x+2))

\frac{\partial}{\partial x} ((90 - x)^{2} \cdot (x + 2))

3 x^{2} - 356 x + 7740

Solution steps

\frac{\partial}{\partial x} ((90 - x)^{2} (x + 2))

Apply the Product Rule:

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

f = (90 - x)^{2}, g = x + 2

= \frac{\partial}{\partial x} ((90 - x)^{2}) (x + 2) + \frac{\partial}{\partial x} (x + 2) (90 - x)^{2}

\frac{\partial}{\partial x} ((90 - x)^{2}) = - 2 (90 - x)

\frac{\partial}{\partial x} (x + 2) = 1

= (- 2 (90 - x)) (x + 2) + 1 \cdot (90 - x)^{2}

Simplify

(- 2 (90 - x)) (x + 2) + 1 \cdot (90 - x)^{2} : 3 x^{2} - 356 x + 7740

= 3 x^{2} - 356 x + 7740

\int \frac{3}{2 x 9 x ^{2} - 1} d x

f (x) = 1 4^{x}

\int_{1}^{4} \frac{1}{x - 4} d x

4 t - 10

\int \frac{1}{x x ^{2} - 4} d x

What is (\partial)/(\partial x)((90-x)^2*(x+2)) ?
The answer to (\partial)/(\partial x)((90-x)^2*(x+2)) is 3x^2-356x+7740