What is the derivative of (1-2x/(3+x)) ?

The derivative of (1-2x/(3+x)) is -7/((3+x)^2)

What is the first derivative of (1-2x/(3+x)) ?

The first derivative of (1-2x/(3+x)) is -7/((3+x)^2)

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

- \frac{7}{( 3 + x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (1 - 2 x) = - 2

\frac{d}{d x} (3 + x) = 1

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

Simplify

\frac{( - 2 ) ( 3 + x ) - 1 \cdot ( 1 - 2 x )}{( 3 + x ) ^{2}} : - \frac{7}{( 3 + x ) ^{2}}

= - \frac{7}{( 3 + x ) ^{2}}

\frac{d}{d x} (cos (x^{5}))

\int e^{x - e^{x}} d x

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

\int \frac{r ^{2} - 10 r + 4}{r ^{3}} d r

y^{^{'}} + y = sin (t), y (0) = - 1

What is the derivative of (1-2x/(3+x)) ?
The derivative of (1-2x/(3+x)) is -7/((3+x)^2)
What is the first derivative of (1-2x/(3+x)) ?
The first derivative of (1-2x/(3+x)) is -7/((3+x)^2)