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3.22 Examples of chain rule

Example

Find (i) ${{d}\over{dx}}\sin^{3}x$ and (ii) ${{d}\over{dx}}e^{-x^{2}};$

then find the derivatives of

(iii)\quad f(x)={{e^{x^{3}}}\over{x^{2}}}\qquad(iv)\quad g(x)={{e^{\sin x}}% \over{\cos x}}.

Express the answer in the original variables.