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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

\int 2 t^{2} d t

cos (3 t + 5) e^{2 t}

\int \frac{1}{1 - x ^{2}} ln (\frac{1 + x}{1 - x}) d x

\int_{0}^{\frac{π}{3}} sin (x) d x

y = ln (x + x^{2} + 9)

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