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

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

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

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

e^{y^{2}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

= e^{y^{2}} (1 + 0)

Simplify

= e^{y^{2}}

2 cos (2 x)

f (x) = \frac{ln ( x ^{2} )}{x}

f (x) = e^{- 5 x} cos (3 x)

\frac{d}{d x} (sin (x + sin (2 x)))

\int_{- 1}^{2} (x + 2) - (x^{2}) d x

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