What is (\partial)/(\partial y)(e^ysin(x)) ?

The answer to (\partial)/(\partial y)(e^ysin(x)) is sin(x)e^y

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(\partial)/(\partial y)(e^ysin(x))

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

sin (x) e^{y}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

= sin (x) e^{y}

\frac{( 4 s - 18 )}{s ^{2} - 6 s + 10}

\frac{d y}{d t} = - 3 y + 4 cos (2 t)

(7 x y^{2} - 2 y) + (7 x^{2} y - 2 x) y^{^{'}} = 0

\int 20 x d x

What is (\partial)/(\partial y)(e^ysin(x)) ?
The answer to (\partial)/(\partial y)(e^ysin(x)) is sin(x)e^y