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

The answer to (\partial)/(\partial x)(-(2y)/(3+2x)) is (4y)/((3+2x)^2)

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

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

\frac{4 y}{( 3 + 2 x ) ^{2}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

- 2 y (- \frac{1}{( 3 + 2 x ) ^{2}} \cdot 2) : \frac{4 y}{( 3 + 2 x ) ^{2}}

= \frac{4 y}{( 3 + 2 x ) ^{2}}

\int \frac{- 28}{x ^{2} x ^{2} + 25} d x

x \to 10 lim (\frac{1}{x - 10})

n = 1 \sum \infty (- \frac{3}{2})^{n}

\int_{- 1}^{0} x - 2 d x

\int \frac{1}{x ( x + 1 ) ( x - 2 )} d x

What is (\partial)/(\partial x)(-(2y)/(3+2x)) ?
The answer to (\partial)/(\partial x)(-(2y)/(3+2x)) is (4y)/((3+2x)^2)