What is (\partial)/(\partial y)(sin(x)+x^2e^y-1) ?

The answer to (\partial)/(\partial y)(sin(x)+x^2e^y-1) is e^yx^2

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(\partial)/(\partial y)(sin(x)+x^2e^y-1)

\frac{\partial}{\partial y} (sin (x) + x^{2} e^{y} - 1)

e^{y} x^{2}

Solution steps

\frac{\partial}{\partial y} (sin (x) + x^{2} e^{y} - 1)

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (sin (x)) + \frac{\partial}{\partial y} (x^{2} e^{y}) - \frac{\partial}{\partial y} (1)

\frac{\partial}{\partial y} (sin (x)) = 0

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

\frac{\partial}{\partial y} (1) = 0

= 0 + x^{2} e^{y} - 0

Simplify

= e^{y} x^{2}

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What is (\partial)/(\partial y)(sin(x)+x^2e^y-1) ?
The answer to (\partial)/(\partial y)(sin(x)+x^2e^y-1) is e^yx^2