Home page for accesible maths Math 101 Chapter 3: Differentiation

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3.22 Examples of chain rule

Example

Find (i) dd⁢x⁢sin3⁡x{{d}\over{dx}}\sin^{3}x and (ii) dd⁢x⁢e-x2;{{d}\over{dx}}e^{-x^{2}};

then find the derivatives of

(i⁢i⁢i) f⁢(x)=ex3x2  (i⁢v) g⁢(x)=esin⁡xcos⁡x.(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.