What is (\partial)/(\partial y)(5/2 x^2+4xy) ?

The answer to (\partial)/(\partial y)(5/2 x^2+4xy) is 4x

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(\partial)/(\partial y)(5/2 x^2+4xy)

\frac{\partial}{\partial y} (\frac{5}{2} x^{2} + 4 x y)

4 x

Solution steps

\frac{\partial}{\partial y} (\frac{5}{2} x^{2} + 4 x y)

Simplify

\frac{5}{2} x^{2} + 4 x y : \frac{5 x ^{2}}{2} + 4 x y

= \frac{\partial}{\partial y} (\frac{5 x ^{2}}{2} + 4 x y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (\frac{5 x ^{2}}{2}) + \frac{\partial}{\partial y} (4 x y)

\frac{\partial}{\partial y} (\frac{5 x ^{2}}{2}) = 0

\frac{\partial}{\partial y} (4 x y) = 4 x

= 0 + 4 x

Simplify

= 4 x

\int \frac{t}{1 - t ^{8}} d t

\frac{\partial}{\partial x} ((x - y)^{10})

x^{4}, x^{2}

f (x) = d e^{- c x}

\int \frac{1 - x ^{2}}{2 x} d x

What is (\partial)/(\partial y)(5/2 x^2+4xy) ?
The answer to (\partial)/(\partial y)(5/2 x^2+4xy) is 4x