What is the derivative of (3-2x/(3+2x)) ?

The derivative of (3-2x/(3+2x)) is -(12)/((3+2x)^2)

What is the first derivative of (3-2x/(3+2x)) ?

The first derivative of (3-2x/(3+2x)) is -(12)/((3+2x)^2)

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\frac{d}{d x} (\frac{3 - 2 x}{3 + 2 x})

- \frac{12}{( 3 + 2 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 - 2 x}{3 + 2 x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (3 - 2 x) = - 2

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

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

Simplify

\frac{( - 2 ) ( 3 + 2 x ) - 2 ( 3 - 2 x )}{( 3 + 2 x ) ^{2}} : - \frac{12}{( 3 + 2 x ) ^{2}}

= - \frac{12}{( 3 + 2 x ) ^{2}}

\int x^{4} sin (3 x) d x

\int - (x^{2} + 2) e^{x} d x

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

f (x) = 2^{70}

\int \frac{x ^{5} - 3 x ^{2} + 4}{x} d x

What is the derivative of (3-2x/(3+2x)) ?
The derivative of (3-2x/(3+2x)) is -(12)/((3+2x)^2)
What is the first derivative of (3-2x/(3+2x)) ?
The first derivative of (3-2x/(3+2x)) is -(12)/((3+2x)^2)