What is (\partial)/(\partial x)((x^2-3y)(x-2)) ?

The answer to (\partial)/(\partial x)((x^2-3y)(x-2)) is 3x^2-4x-3y

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(\partial)/(\partial x)((x^2-3y)(x-2))

\frac{\partial}{\partial x} ((x^{2} - 3 y) (x - 2))

3 x^{2} - 4 x - 3 y

Solution steps

\frac{\partial}{\partial x} ((x^{2} - 3 y) (x - 2))

Treat

y

as a constant

Apply the Product Rule:

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

f = x^{2} - 3 y, g = x - 2

= \frac{\partial}{\partial x} (x^{2} - 3 y) (x - 2) + \frac{\partial}{\partial x} (x - 2) (x^{2} - 3 y)

\frac{\partial}{\partial x} (x^{2} - 3 y) = 2 x

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

= 2 x (x - 2) + 1 \cdot (x^{2} - 3 y)

Simplify

2 x (x - 2) + 1 \cdot (x^{2} - 3 y) : 3 x^{2} - 4 x - 3 y

= 3 x^{2} - 4 x - 3 y

\frac{\partial}{\partial y} (\frac{e ^{x}}{e ^{x} + e ^{y}})

\frac{\partial}{\partial x} (5 x^{3} y + 3 sin (x y))

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

\int x \cdot cos (x^{2} + 1) d x

\int \frac{3 x - 1}{4 x ^{2} - 4 x + 17} d x

What is (\partial)/(\partial x)((x^2-3y)(x-2)) ?
The answer to (\partial)/(\partial x)((x^2-3y)(x-2)) is 3x^2-4x-3y