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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x + 2 y}, g = sin (y)

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

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

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

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

g (x) = x^{2}, [0, 1]

x \to \infty lim (4 x - 1)

\int_{0}^{l n (3)} \frac{e ^{t}}{e ^{2 t} + 49} d t

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

y^{^{''}} + 81 y = 0

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