What is (\partial)/(\partial y)(x^3y+e^{xy^2}) ?

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

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(\partial)/(\partial y)(x^3y+e^{xy^2})

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

x^{3} + e^{x y^{2}} \cdot 2 x y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= x^{3} + e^{x y^{2}} \cdot 2 x y

\int_{0}^{1} ln (7 x) d x

n = 0 \sum \infty \frac{( - 1 ) ^{n} 7 ^{n} x ^{n}}{5 ^{n + 1}}

\int_{2}^{\infty} 2 e^{- 2 x} d x

\int 2 b x^{3} d x

\frac{d}{d x} ((5 x^{2} - 7) (3 x^{2} - 2 x + 1))

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