What is (\partial)/(\partial x)(ye^{yx}) ?

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

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(\partial)/(\partial x)(ye^{yx})

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

e^{y x} y^{2}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= y e^{y x} y

Simplify

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

= e^{y x} y^{2}

\int \frac{15}{5 x + x x} d x

x \to 0 + lim (\frac{x + 3}{x ^{2}})

ln (\frac{5 x ^{2} + x + 6}{x ^{3}})

\int 8 x - cos (x) d x

\frac{d}{d x} (2 cos (x))

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