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

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

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

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

- 2 e^{y^{2}} y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (x^{2}) = 0

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

= 0 - e^{y^{2}} \cdot 2 y

Simplify

= - 2 e^{y^{2}} y

n = 1 \sum \infty \frac{n}{n + 1}

\int - t^{3} d t

\frac{\partial}{\partial y} (- z)

\frac{d}{d x} (sin (x + 1) + 5 x)

\frac{d}{d y} (3 x e^{- \frac{1}{y ^{3}}})

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