What is (\partial)/(\partial x)(e^{xy^2}+4zy^3) ?

The answer to (\partial)/(\partial x)(e^{xy^2}+4zy^3) is e^{xy^2}y^2

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(\partial)/(\partial x)(e^{xy^2}+4zy^3)

\frac{\partial}{\partial x} (e^{x y^{2}} + 4 z y^{3})

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

Solution steps

\frac{\partial}{\partial x} (e^{x y^{2}} + 4 z y^{3})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (e^{x y^{2}}) + \frac{\partial}{\partial x} (4 z y^{3})

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

\frac{\partial}{\partial x} (4 z y^{3}) = 0

= e^{x y^{2}} y^{2} + 0

Simplify

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

(1 + x^{2}) \frac{d y}{d x} + x y = 0

y = x^{- \frac{1}{2}}

\frac{d}{d x} (x^{2} \cdot y^{2})

\int \frac{1}{9 - 16 x ^{2}} d x

\frac{d}{d x} (3 x^{4} - 2 x^{3} + 1)

What is (\partial)/(\partial x)(e^{xy^2}+4zy^3) ?
The answer to (\partial)/(\partial x)(e^{xy^2}+4zy^3) is e^{xy^2}y^2