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

The answer to (\partial)/(\partial x)(e^{xy}+1/(x+y)) is e^{xy}y-1/((x+y)^2)

Popular >

(\partial)/(\partial x)(e^{xy}+1/(x+y))

\frac{\partial}{\partial x} (e^{x y} + \frac{1}{x + y})

e^{x y} y - \frac{1}{( x + y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (e^{x y} + \frac{1}{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} (\frac{1}{x + y})

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

\frac{\partial}{\partial x} (\frac{1}{x + y}) = - \frac{1}{( x + y ) ^{2}}

= e^{x y} y - \frac{1}{( x + y ) ^{2}}

4 x^{2} + 2 x - 1

f (x) = (5 x^{6} + 4 x^{3})^{4}

\frac{\partial}{\partial x} (ln (8 x + 7 y))

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y = x e^{x}

\int_{1}^{5} \frac{x}{x ^{2} + 6 x + 13} d x

What is (\partial)/(\partial x)(e^{xy}+1/(x+y)) ?
The answer to (\partial)/(\partial x)(e^{xy}+1/(x+y)) is e^{xy}y-1/((x+y)^2)