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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\int_{- 7}^{7} \frac{y}{49 - y ^{2}} d y

4 arcsin (x^{3})

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n = 1 \sum \infty \frac{1}{n ^{1.1}}

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