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

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

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

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

cos (x) + e^{x y} y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (sin (x)) = cos (x)

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

= cos (x) + e^{x y} y

\int \frac{( 5 x - 12 )}{x ^{3} - 6 x ^{2} + 8 x} d x

x \to 1 - lim (\frac{3}{x ^{3} - 1})

x y^{^{'}} + y = 6 x y^{2}, y (1) = - 8

\int_{2}^{13} \frac{1}{x ^{3} - 8} d x

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

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