What is (\partial)/(\partial x)(x(20-2x)(16-2x)) ?

The answer to (\partial)/(\partial x)(x(20-2x)(16-2x)) is 12x^2-144x+320

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(\partial)/(\partial x)(x(20-2x)(16-2x))

\frac{\partial}{\partial x} (x (20 - 2 x) (16 - 2 x))

12 x^{2} - 144 x + 320

Solution steps

\frac{\partial}{\partial x} (x (20 - 2 x) (16 - 2 x))

Apply the Product Rule:

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

f = x, g = (20 - 2 x) (16 - 2 x)

= \frac{\partial}{\partial x} (x) (20 - 2 x) (16 - 2 x) + \frac{\partial}{\partial x} ((20 - 2 x) (16 - 2 x)) x

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

\frac{\partial}{\partial x} ((20 - 2 x) (16 - 2 x)) = 8 x - 72

= 1 \cdot (20 - 2 x) (16 - 2 x) + (8 x - 72) x

Simplify

1 \cdot (20 - 2 x) (16 - 2 x) + (8 x - 72) x : 12 x^{2} - 144 x + 320

= 12 x^{2} - 144 x + 320

\frac{\partial}{\partial x} (x^{9} y^{9} - x^{8} y^{8})

\int 2 x^{2} e^{x^{3}} d x

\int \frac{1}{sec ^{4} ( \frac{1}{4} x )} d x

e^{x} + 0 + 5

x \to 2 lim (8 - 2 x^{2})

What is (\partial)/(\partial x)(x(20-2x)(16-2x)) ?
The answer to (\partial)/(\partial x)(x(20-2x)(16-2x)) is 12x^2-144x+320