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

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

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

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

- sin (2 x) e^{2 y} \cdot 2

Solution steps

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

Simplify

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

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

f (x) = (2 x + 3)^{11} (4 - 5 x)^{9}

x \to 1 + lim (1)

\frac{9}{10} x^{2} d y - 18 d x = 0

\frac{\partial}{\partial x} (x^{3} + x^{2} y - y^{2} - 4 y)

\frac{d}{d x} (4 x + 5)

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