What is (\partial)/(\partial y)((y-x^2)^2+x^5) ?

The answer to (\partial)/(\partial y)((y-x^2)^2+x^5) is 2(y-x^2)

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(\partial)/(\partial y)((y-x^2)^2+x^5)

\frac{\partial}{\partial y} ((y - x^{2})^{2} + x^{5})

2 (y - x^{2})

Solution steps

\frac{\partial}{\partial y} ((y - x^{2})^{2} + x^{5})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} ((y - x^{2})^{2}) + \frac{\partial}{\partial y} (x^{5})

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

\frac{\partial}{\partial y} (x^{5}) = 0

= 2 (y - x^{2}) + 0

Simplify

= 2 (y - x^{2})

\frac{d}{d x} (22 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x))

\int_{0}^{1} (x) d x

\int \frac{3 ( 1 - tan ^{2} ( x ) )}{sec ^{2} ( x )} d x

2 x sin (x^{2})

\frac{d}{d x} (\frac{b a ^{2} - x ^{2}}{a})

What is (\partial)/(\partial y)((y-x^2)^2+x^5) ?
The answer to (\partial)/(\partial y)((y-x^2)^2+x^5) is 2(y-x^2)