What is the derivative of f(x)=(1/x-1/a)^2 ?

The derivative of f(x)=(1/x-1/a)^2 is -(2(a-x))/(ax^3)

What is the first derivative of f(x)=(1/x-1/a)^2 ?

The first derivative of f(x)=(1/x-1/a)^2 is -(2(a-x))/(ax^3)

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derivative of

f (x) = (\frac{1}{x} - \frac{1}{a})^{2}

- \frac{2 ( a - x )}{a x ^{3}}

Solution steps

\frac{d}{d x} ((\frac{1}{x} - \frac{1}{a})^{2})

Apply the chain rule:

2 (\frac{1}{x} - \frac{1}{a}) \frac{d}{d x} (\frac{1}{x} - \frac{1}{a})

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

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

= 2 (\frac{1}{x} - \frac{1}{a}) (- \frac{1}{x ^{2}})

Simplify

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

= - \frac{2 ( a - x )}{a x ^{3}}

\frac{7}{x}

\frac{d}{d x} (cosh (cos (x)))

x \to 0 lim (\frac{sin ( 2 x )}{arcsin ( x )})

\frac{d}{d x} ((x^{2} + 5)^{7})

f (x) = ln (e^{- x} + x e^{- x})

What is the derivative of f(x)=(1/x-1/a)^2 ?
The derivative of f(x)=(1/x-1/a)^2 is -(2(a-x))/(ax^3)
What is the first derivative of f(x)=(1/x-1/a)^2 ?
The first derivative of f(x)=(1/x-1/a)^2 is -(2(a-x))/(ax^3)