What is (\partial)/(\partial x)(e^{(2x+3y)/(3y)}) ?

The answer to (\partial)/(\partial x)(e^{(2x+3y)/(3y)}) is (2e^{\frac{2x+3y)/(3y)}}{3y}

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(\partial)/(\partial x)(e^{(2x+3y)/(3y)})

\frac{\partial}{\partial x} (e^{\frac{2 x + 3 y}{3 y}})

\frac{2 e ^{\frac{2 x + 3 y}{3 y}}}{3 y}

Solution steps

\frac{\partial}{\partial x} (e^{\frac{2 x + 3 y}{3 y}})

Treat

y

as a constant

Apply the chain rule:

e^{\frac{2 x + 3 y}{3 y}} \frac{\partial}{\partial x} (\frac{2 x + 3 y}{3 y})

= e^{\frac{2 x + 3 y}{3 y}} \frac{\partial}{\partial x} (\frac{2 x + 3 y}{3 y})

\frac{\partial}{\partial x} (\frac{2 x + 3 y}{3 y}) = \frac{2}{3 y}

= e^{\frac{2 x + 3 y}{3 y}} \frac{2}{3 y}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 e ^{\frac{2 x + 3 y}{3 y}}}{3 y}

\frac{d}{d x} (5 (e^{x})^{- 4})

x \to 2 lim (12 x^{2})

x \to - 2 lim (\frac{∣ x + 2 ∣}{x + 2})

\int \frac{sech ( \frac{1}{x} ) tanh ( \frac{1}{x} )}{x ^{2}} d x

\int \frac{1}{9 + t ^{2}} d t

What is (\partial)/(\partial x)(e^{(2x+3y)/(3y)}) ?
The answer to (\partial)/(\partial x)(e^{(2x+3y)/(3y)}) is (2e^{\frac{2x+3y)/(3y)}}{3y}