What is (\partial)/(\partial x)(3/(2x+3y)) ?

The answer to (\partial)/(\partial x)(3/(2x+3y)) is -6/((2x+3y)^2)

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(\partial)/(\partial x)(3/(2x+3y))

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

- \frac{6}{( 2 x + 3 y ) ^{2}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 3 \frac{\partial}{\partial x} (\frac{1}{2 x + 3 y})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 3 \frac{\partial}{\partial x} ((2 x + 3 y)^{- 1})

Apply the chain rule:

- \frac{1}{( 2 x + 3 y ) ^{2}} \frac{\partial}{\partial x} (2 x + 3 y)

= - \frac{1}{( 2 x + 3 y ) ^{2}} \frac{\partial}{\partial x} (2 x + 3 y)

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

= 3 (- \frac{1}{( 2 x + 3 y ) ^{2}} \cdot 2)

Simplify

3 (- \frac{1}{( 2 x + 3 y ) ^{2}} \cdot 2) : - \frac{6}{( 2 x + 3 y ) ^{2}}

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

x \to - 4 lim ((x + 3)^{2})

\int \frac{x}{x ^{2} + x + 1} d x

\frac{d}{d x} (- e^{3 x})

\frac{( 6 x ^{2} + 2 x + 6 )}{x}

\int r^{2} (r^{3} + 6)^{3} d r

What is (\partial)/(\partial x)(3/(2x+3y)) ?
The answer to (\partial)/(\partial x)(3/(2x+3y)) is -6/((2x+3y)^2)