What is the derivative of (1-5x/(3+x)) ?

The derivative of (1-5x/(3+x)) is -(16)/((3+x)^2)

What is the first derivative of (1-5x/(3+x)) ?

The first derivative of (1-5x/(3+x)) is -(16)/((3+x)^2)

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\frac{d}{d x} (\frac{1 - 5 x}{3 + x})

- \frac{16}{( 3 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 - 5 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 - 5 x ) ( 3 + x ) - \frac{d}{d x} ( 3 + x ) ( 1 - 5 x )}{( 3 + x ) ^{2}}

\frac{d}{d x} (1 - 5 x) = - 5

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

= \frac{( - 5 ) ( 3 + x ) - 1 \cdot ( 1 - 5 x )}{( 3 + x ) ^{2}}

Simplify

\frac{( - 5 ) ( 3 + x ) - 1 \cdot ( 1 - 5 x )}{( 3 + x ) ^{2}} : - \frac{16}{( 3 + x ) ^{2}}

= - \frac{16}{( 3 + x ) ^{2}}

\frac{\partial}{\partial x} (x arctan (\frac{y}{z}))

f (r) = e^{r} + x^{e}

0.1 x^{3} - 0.1 x^{2} + 50 x

\frac{d}{d y} (e^{x + y})

f (x) = \frac{x}{3 x - 4 ln ( x )}

What is the derivative of (1-5x/(3+x)) ?
The derivative of (1-5x/(3+x)) is -(16)/((3+x)^2)
What is the first derivative of (1-5x/(3+x)) ?
The first derivative of (1-5x/(3+x)) is -(16)/((3+x)^2)