What is (\partial)/(\partial x)((x^2+xy)^3) ?

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

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(\partial)/(\partial x)((x^2+xy)^3)

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

2 x y d x + x^{2} d y = 0

x \to 3 + lim (x^{2} + 2 x)

\frac{d y}{d x} = \frac{( 5 y )}{( 2 x + 3 ) ( 3 x + 2 )}

0.125 y^{^{''}} + 4 y^{^{'}} + 20 y = 0

\frac{\partial}{\partial y} (\frac{x}{1 + x ^{2} + y ^{2}})

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