What is the derivative of 14*((-x+2)/(x^2)) ?

The derivative of 14*((-x+2)/(x^2)) is -(14(-x+4))/(x^3)

What is the first derivative of 14*((-x+2)/(x^2)) ?

The first derivative of 14*((-x+2)/(x^2)) is -(14(-x+4))/(x^3)

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derivative of

14 \cdot (\frac{- x + 2}{x ^{2}})

- \frac{14 ( - x + 4 )}{x ^{3}}

Solution steps

\frac{d}{d x} (14 \cdot \frac{- x + 2}{x ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 14 \frac{d}{d x} (\frac{- x + 2}{x ^{2}})

Apply the Quotient Rule:

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

= 14 \cdot \frac{\frac{d}{d x} ( - x + 2 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( - x + 2 )}{( x ^{2} ) ^{2}}

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

\frac{d}{d x} (x^{2}) = 2 x

= 14 \cdot \frac{( - 1 ) x ^{2} - 2 x ( - x + 2 )}{( x ^{2} ) ^{2}}

Simplify

14 \cdot \frac{( - 1 ) x ^{2} - 2 x ( - x + 2 )}{( x ^{2} ) ^{2}} : - \frac{14 ( - x + 4 )}{x ^{3}}

= - \frac{14 ( - x + 4 )}{x ^{3}}

What is the derivative of 14*((-x+2)/(x^2)) ?
The derivative of 14*((-x+2)/(x^2)) is -(14(-x+4))/(x^3)
What is the first derivative of 14*((-x+2)/(x^2)) ?
The first derivative of 14*((-x+2)/(x^2)) is -(14(-x+4))/(x^3)