Solve f(x)=k/x a - ScanMath

Evaluate

f (x) = \frac{k}{x} \times a

Simplify

f (x) = \frac{ka}{x}

Take the derivative of both sides

f^{'} (x) = \frac{d}{d x} (\frac{ka}{x})

Use differentiation rules

f^{'} (x) = ka \times \frac{d}{d x} (\frac{1}{x})

Rewrite the expression in exponential form

f^{'} (x) = ka \times \frac{d}{d x} (x^{- 1})

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

f^{'} (x) = ka (- x^{- 2})

Express with a positive exponent using a^{- n} = \frac{1}{a ^{n}}

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

Solution

f^{'} (x) = - \frac{ak}{x ^{2}}

Function