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

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

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

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

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derivative of

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

- \frac{16}{( 5 + x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= - \frac{16}{( 5 + x ) ^{2}}

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