f-x-x-2-x-1-sin2x-f-x-

Question Number 11150 by suci last updated on 14/Mar/17

f (x) = {(x^{2} + x + 1)}^{s i n 2 x}

f^{'} (x) = \dots ? ? ?

Answered by ajfour last updated on 14/Mar/17

= {(x^{2} + x + 1)}^{\sin 2 x} {(2 \cos 2 x) \ln (x^{2} + x + 1)

+ \frac{(2 x + 1)}{(x^{2} + x + 1)} \sin 2 x}

Commented by ajfour last updated on 14/Mar/17

t a k i n g l o g a n d d i f f e r e n t i a t e :

y = g {(x)}^{h (x)} \Rightarrow \ln y = h (x) \ln g (x)

\frac{1}{y} \frac{d y}{d x} = h^{'} (x) \ln g (x) + h (x) g^{'} (x) / g (x)

\frac{d y}{d x} = g {(x)}^{h (x)} [h^{'} (x) \ln g (x) + h (x) \frac{g^{'} (x)}{g (x)}]

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