How do you differentiate sqrt(sin^3(1/x^2)  using the chain rule?

Jan 2, 2016

Always convert to exponents first ...

Explanation:

$\frac{d}{\mathrm{dx}} {\left[{\left(\sin \left({x}^{-} 2\right)\right)}^{3}\right]}^{\frac{1}{2}}$

$= \left(\frac{1}{2}\right) {\left[{\left(\sin \left({x}^{-} 2\right)\right)}^{3}\right]}^{- \frac{1}{2}} \left(3\right) {\left(\sin \left({x}^{-} 2\right)\right)}^{2} \left(\cos \left({x}^{-} 2\right)\right) \left(- 2 {x}^{-} 3\right)$

$= - 3 {x}^{-} 3 {\left[{\left(\sin \left({x}^{-} 2\right)\right)}^{3}\right]}^{- \frac{1}{2}} {\left(\sin \left({x}^{-} 2\right)\right)}^{2} \left(\cos \left({x}^{-} 2\right)\right)$

hope that helped