What is the derivative of x/(x^{-1+9}) ?

The derivative of x/(x^{-1+9}) is (x(9x+2))/((1+9x)^2)

What is the first derivative of x/(x^{-1+9}) ?

The first derivative of x/(x^{-1+9}) is (x(9x+2))/((1+9x)^2)

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\frac{d}{d x} (\frac{x}{x ^{- 1} + 9})

\frac{x ( 9 x + 2 )}{( 1 + 9 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{- 1} + 9})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{- 1} + 9 ) - \frac{d}{d x} ( x ^{- 1} + 9 ) x}{( x ^{- 1} + 9 ) ^{2}}

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

\frac{d}{d x} (x^{- 1} + 9) = - \frac{1}{x ^{2}}

= \frac{1 \cdot ( x ^{- 1} + 9 ) - ( - \frac{1}{x ^{2}} ) x}{( x ^{- 1} + 9 ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{- 1} + 9 ) - ( - \frac{1}{x ^{2}} ) x}{( x ^{- 1} + 9 ) ^{2}} : \frac{x ( 9 x + 2 )}{( 1 + 9 x ) ^{2}}

= \frac{x ( 9 x + 2 )}{( 1 + 9 x ) ^{2}}

\int (\frac{3 x ^{2}}{64 - x ^{2}}) d x

x \to 0 + lim (\frac{x ^{- 2}}{x})

\int x 36 - x^{2} d x

\int \frac{e ^{t}}{( 1 + e ^{(2 t)} ) ^{(\frac{3}{2})}} d t

\int 3 x - 2 d x

What is the derivative of x/(x^{-1+9}) ?
The derivative of x/(x^{-1+9}) is (x(9x+2))/((1+9x)^2)
What is the first derivative of x/(x^{-1+9}) ?
The first derivative of x/(x^{-1+9}) is (x(9x+2))/((1+9x)^2)