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

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

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(\partial)/(\partial x)(x^2ye^{y/z})

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

2 e^{\frac{y}{z}} x y

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 2 e^{\frac{y}{z}} x y

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

x \to \infty lim (4 x^{3} (e^{- \frac{2}{x ^{3}}} - 1))

\int sin^{4} (d) x d x

x = y^{2} + 6, y = \frac{x}{2} - \frac{3}{2}

t \to 0 lim (cos (t) sin (t))

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