What is (\partial)/(\partial y)((ye^x)^2) ?

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

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(\partial)/(\partial y)((ye^x)^2)

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

2 e^{2 x} y

Solution steps

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

Simplify

(y e^{x})^{2} : e^{2 x} y^{2}

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= e^{2 x} \cdot 2 y^{2 - 1}

Simplify

= 2 e^{2 x} y

f (x) = (x^{- 2} + x)^{3} (4 x)^{- 2 x}

\int sin (8 x) ln (sin (8 x)) d x

\int \frac{cos ( x ) - x sin ( x )}{x cos ( x )} d x

\frac{d}{d x} (ln (\frac{x + x ^{2} + 4}{2}))

f (x) = e^{x} - x - 2

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