What is (\partial)/(\partial y)(e^{xy}cos(x^2)) ?

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

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(\partial)/(\partial y)(e^{xy}cos(x^2))

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

cos (x^{2}) e^{x y} x

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= cos (x^{2}) e^{x y} x

n = 1 \sum \infty \frac{3}{n ^{2} + 5}

\int sec (6 x) d x

\int x^{2} e^{- 10 x} d x

\int - \frac{1}{x ^{3}} d x

x \to 5 + lim (I n (x^{2} - 25))

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