What is the derivative of x/(x^{-1)+12} ?

The derivative of x/(x^{-1)+12} is (x(12x+2))/((1+12x)^2)

What is the first derivative of x/(x^{-1)+12} ?

The first derivative of x/(x^{-1)+12} is (x(12x+2))/((1+12x)^2)

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derivative of

\frac{x}{x ^{- 1} + 12}

\frac{x ( 12 x + 2 )}{( 1 + 12 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{- 1} + 12})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{- 1} + 12 ) - \frac{d}{d x} ( x ^{- 1} + 12 ) x}{( x ^{- 1} + 12 ) ^{2}}

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

\frac{d}{d x} (x^{- 1} + 12) = - \frac{1}{x ^{2}}

= \frac{1 \cdot ( x ^{- 1} + 12 ) - ( - \frac{1}{x ^{2}} ) x}{( x ^{- 1} + 12 ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{- 1} + 12 ) - ( - \frac{1}{x ^{2}} ) x}{( x ^{- 1} + 12 ) ^{2}} : \frac{x ( 12 x + 2 )}{( 1 + 12 x ) ^{2}}

= \frac{x ( 12 x + 2 )}{( 1 + 12 x ) ^{2}}

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

\frac{\partial}{\partial x} (e^{- x} \cdot y)

arcsec (2 x)

\int \frac{x + 2}{x ^{2} - 2 x - 15} d x

x \to 1 lim (3 (x - 1)^{2})

What is the derivative of x/(x^{-1)+12} ?
The derivative of x/(x^{-1)+12} is (x(12x+2))/((1+12x)^2)
What is the first derivative of x/(x^{-1)+12} ?
The first derivative of x/(x^{-1)+12} is (x(12x+2))/((1+12x)^2)