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

The answer to (\partial)/(\partial x)(e^{xy}+ln(x/y)) is e^{xy}y+1/x

Popular >

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

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

e^{x y} y + \frac{1}{x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (ln (\frac{x}{y})) = \frac{1}{x}

= e^{x y} y + \frac{1}{x}

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

w \to \infty lim (\frac{2 w ^{2} - 3 w + 4}{5 w ^{2} + 7 w - 1})

y^{^{''}} - k y = 0

x \to - 2 lim ((x - 6)^{\frac{2}{3}})

y^{^{'}} = 0.2 ln (\frac{2000}{y}) y

What is (\partial)/(\partial x)(e^{xy}+ln(x/y)) ?
The answer to (\partial)/(\partial x)(e^{xy}+ln(x/y)) is e^{xy}y+1/x