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

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

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

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

e^{x y^{2}} y^{2}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{x y^{2}} y^{2}

\frac{d}{d x} (\frac{6}{x + 3})

\frac{\frac{10}{6}}{s + 6}

\int_{0}^{2 π} cos (θ) d θ

\frac{\partial}{\partial t} (\frac{s - 2 r}{t})

\frac{y ^{3}}{27} + \frac{9}{4 y}

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