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

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

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(\partial)/(\partial y)(2x^3y+cos(x^2))

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

2 x^{3}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 x^{3} + 0

Simplify

= 2 x^{3}

\frac{d}{d x} (C e^{3 x})

\int \frac{1}{( x - 1 ) ( x - 3 ) ( x + 4 )} d x

(9 - x^{2})^{^{'}}

f (x) = x e^{x^{2}}

\frac{d}{d x} (240 (1 - \frac{3}{3 + e ^{- 0.5 x}}))

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