What is the derivative of ((x-a(b-x))/(x^2)) ?

The derivative of ((x-a(b-x))/(x^2)) is (-ax-bx+2ab)/(x^3)

What is the first derivative of ((x-a(b-x))/(x^2)) ?

The first derivative of ((x-a(b-x))/(x^2)) is (-ax-bx+2ab)/(x^3)

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\frac{d}{d x} (\frac{( x - a ) ( b - x )}{x ^{2}})

\frac{- a x - b x + 2 ab}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{( x - a ) ( b - x )}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ( x - a ) ( b - x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x - a ) ( b - x )}{( x ^{2} ) ^{2}}

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

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

= \frac{( b - 2 x + a ) x ^{2} - 2 x ( x - a ) ( b - x )}{( x ^{2} ) ^{2}}

Simplify

\frac{( b - 2 x + a ) x ^{2} - 2 x ( x - a ) ( b - x )}{( x ^{2} ) ^{2}} : \frac{- a x - b x + 2 ab}{x ^{3}}

= \frac{- a x - b x + 2 ab}{x ^{3}}

\int \frac{8 e ^{8 s}}{3 + e ^{8 s}} d s

\int \frac{9 e ^{4 t}}{1 + e ^{8 t}} d t

x = 1 \sum \infty \frac{6}{x ^{2} + x}

3 + 2 f (x)

\int_{0}^{7} 3 x^{2} - 30 x + 72 d x

What is the derivative of ((x-a(b-x))/(x^2)) ?
The derivative of ((x-a(b-x))/(x^2)) is (-ax-bx+2ab)/(x^3)
What is the first derivative of ((x-a(b-x))/(x^2)) ?
The first derivative of ((x-a(b-x))/(x^2)) is (-ax-bx+2ab)/(x^3)