What is the derivative of (10x+1)/(x+100) ?

The derivative of (10x+1)/(x+100) is (999)/((x+100)^2)

What is the first derivative of (10x+1)/(x+100) ?

The first derivative of (10x+1)/(x+100) is (999)/((x+100)^2)

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derivative of

\frac{10 x + 1}{x + 100}

\frac{999}{( x + 100 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{10 x + 1}{x + 100})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 10 x + 1 ) ( x + 100 ) - \frac{d}{d x} ( x + 100 ) ( 10 x + 1 )}{( x + 100 ) ^{2}}

\frac{d}{d x} (10 x + 1) = 10

\frac{d}{d x} (x + 100) = 1

= \frac{10 ( x + 100 ) - 1 \cdot ( 10 x + 1 )}{( x + 100 ) ^{2}}

Simplify

\frac{10 ( x + 100 ) - 1 \cdot ( 10 x + 1 )}{( x + 100 ) ^{2}} : \frac{999}{( x + 100 ) ^{2}}

= \frac{999}{( x + 100 ) ^{2}}

What is the derivative of (10x+1)/(x+100) ?
The derivative of (10x+1)/(x+100) is (999)/((x+100)^2)
What is the first derivative of (10x+1)/(x+100) ?
The first derivative of (10x+1)/(x+100) is (999)/((x+100)^2)