What is (\partial)/(\partial x)((x+y)^3-12xy) ?

The answer to (\partial)/(\partial x)((x+y)^3-12xy) is 3(x+y)^2-12y

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(\partial)/(\partial x)((x+y)^3-12xy)

\frac{\partial}{\partial x} ((x + y)^{3} - 12 x y)

3 (x + y)^{2} - 12 y

Solution steps

\frac{\partial}{\partial x} ((x + y)^{3} - 12 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} ((x + y)^{3}) - \frac{\partial}{\partial x} (12 x y)

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

\frac{\partial}{\partial x} (12 x y) = 12 y

= 3 (x + y)^{2} - 12 y

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

y^{^{'}} = - 5 y

f (x) = \frac{11}{( 2 x ^{3} - 5 ) ^{4}}

\int \frac{3 x}{2 x + 4} d x

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{9}{x ^{4}}) (x + 7 x^{3}))

What is (\partial)/(\partial x)((x+y)^3-12xy) ?
The answer to (\partial)/(\partial x)((x+y)^3-12xy) is 3(x+y)^2-12y