What is the derivative of x/(x^{-1+3}) ?

The derivative of x/(x^{-1+3}) is (x(3x+2))/((1+3x)^2)

What is the first derivative of x/(x^{-1+3}) ?

The first derivative of x/(x^{-1+3}) is (x(3x+2))/((1+3x)^2)

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

\frac{x ( 3 x + 2 )}{( 1 + 3 x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (cos (\frac{3}{2} x))

n = 1 \sum \infty \frac{1 6 ^{\frac{n}{2}}}{2 ^{2 n}}

\int \frac{1}{e ^{- y}} d y

d y = 2 x (y^{2} + 9) d x

\int 0.6 x d x

What is the derivative of x/(x^{-1+3}) ?
The derivative of x/(x^{-1+3}) is (x(3x+2))/((1+3x)^2)
What is the first derivative of x/(x^{-1+3}) ?
The first derivative of x/(x^{-1+3}) is (x(3x+2))/((1+3x)^2)