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

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

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

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

e^{y x} + y e^{y x} x + \frac{1}{y ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

f (x) = x, at x = 64

4 x y y^{^{'}} = 4 y^{2} + 3 x x^{2} + y^{2}

\int (\frac{5}{x} + \frac{12}{x ^{5}}) d x

f (x) = x (x - 1)

\int \frac{x ^{2}}{( 49 - x ^{2} ) ^{\frac{3}{2}}} d x

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