can someone help me please to find the derivative of the next equation :
f(x) = (1/x)*sin(x^(1/3))
f '(x) = ?
thnx
$\displaystyle f(x) = \frac{sin(x^{\frac{1}{3}})}{x}$
Use the quotient rule and bear in mind you'll need to use the chain rule on the numerator
Quotient Rule $\displaystyle \frac{dy}{dx} = \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2}$
Chain Rule: $\displaystyle \frac{d}{dx}f[g(x)] = f'[g(x)] \times g'(x)$