What is (\partial)/(\partial x)(xe^{y^2}+yln(x)) ?

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

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(\partial)/(\partial x)(xe^{y^2}+yln(x))

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

e^{y^{2}} + \frac{y}{x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= e^{y^{2}} + \frac{y}{x}

f (x) = (2 x - 3) \cdot x

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

\int \frac{e ^{x}}{e ^{x} + 1 + 1} d x

\int \frac{( 2 x + 3 ) ^{2}}{x} d x

\frac{d}{d x} (2 sin (x))

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