What is the derivative of x/(x^{-1+4}) ?

The derivative of x/(x^{-1+4}) is (x(4x+2))/((1+4x)^2)

What is the first derivative of x/(x^{-1+4}) ?

The first derivative of x/(x^{-1+4}) is (x(4x+2))/((1+4x)^2)

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\frac{d}{d x} (\frac{x}{x ^{- 1} + 4})

\frac{x ( 4 x + 2 )}{( 1 + 4 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{- 1} + 4})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{- 1} + 4 ) - \frac{d}{d x} ( x ^{- 1} + 4 ) x}{( x ^{- 1} + 4 ) ^{2}}

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

\frac{d}{d x} (x^{- 1} + 4) = - \frac{1}{x ^{2}}

= \frac{1 \cdot ( x ^{- 1} + 4 ) - ( - \frac{1}{x ^{2}} ) x}{( x ^{- 1} + 4 ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{- 1} + 4 ) - ( - \frac{1}{x ^{2}} ) x}{( x ^{- 1} + 4 ) ^{2}} : \frac{x ( 4 x + 2 )}{( 1 + 4 x ) ^{2}}

= \frac{x ( 4 x + 2 )}{( 1 + 4 x ) ^{2}}

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

f (x) = e^{x^{4}}

\frac{\partial}{\partial x} (\frac{1}{x + y + z})

\int \frac{1}{x ^{4} x ^{2} + 4} d x

(x - 3)^{- 2}

What is the derivative of x/(x^{-1+4}) ?
The derivative of x/(x^{-1+4}) is (x(4x+2))/((1+4x)^2)
What is the first derivative of x/(x^{-1+4}) ?
The first derivative of x/(x^{-1+4}) is (x(4x+2))/((1+4x)^2)