What is the derivative of x/(x^{-1)+7} ?

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

What is the first derivative of x/(x^{-1)+7} ?

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

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derivative of

\frac{x}{x ^{- 1} + 7}

\frac{x ( 7 x + 2 )}{( 1 + 7 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{- 1} + 7})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{- 1} + 7 ) - \frac{d}{d x} ( x ^{- 1} + 7 ) x}{( x ^{- 1} + 7 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{- 1} + 7) = - \frac{1}{x ^{2}}

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

Simplify

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

= \frac{x ( 7 x + 2 )}{( 1 + 7 x ) ^{2}}

\int \frac{w ^{3}}{w + 1} d w

\frac{d}{d x} (19 arctan (x))

ln (\frac{6 x ^{2} + 5}{x ^{\frac{4}{5}}})

\frac{s + 4}{s ^{2} + 2 s - 3}

5 x^{2} + 2 x + 6

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