(5/x)^'

Solution

(\frac{5}{x})^{^{'}}

- \frac{5}{x ^{2}}

Solution steps

(\frac{5}{x})^{'}

Take the constant out:

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

= 5 (\frac{1}{x})^{^{'}}

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 5 (x^{- 1})^{^{'}}

Apply the Power Rule:

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

= 5 (- 1 \cdot x^{- 1 - 1})

Simplify

5 (- 1 \cdot x^{- 1 - 1}) : - \frac{5}{x ^{2}}

= - \frac{5}{x ^{2}}

\int sin (3 x) ln (cos (3 x)) d x

\frac{d}{d x} ((4 x^{2} + 2 x - 5) (x^{3} + 7 x + 4))

x \to 1 lim (\frac{x}{x ^{2} - x})

\frac{4 u ^{2}}{( u ^{2} + u ) ^{3}}

f (x) = a cos (2 x) + b sin (2 x)