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

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

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

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

- e^{2 x} sin (y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

= e^{2 x} (- sin (y))

Simplify

= - e^{2 x} sin (y)

\int e^{- x} cos^{2} (x) d x

\int (x 9 - x^{2}) d x

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

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

4 x^{2} y^{2} d x + x^{3} y d y = 0

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