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\frac-2CosxSinx(1+Sin ^2 x)-2Cos ^3 xSinx(1+Sin ^2x) ^2 [/tex] =[/tex] \frac-2CosxSinx-2CosxSin ^3x-2Cos ^3 xSinx (1+Sin ^2x) ^2 [/tex] \frac-2CosxSinx(1+Sin ^2x+Cos ^2 x) (1+Sin ^2x) ^2 = \frac-4CosxSinx(1+Sin ^2 x) ^2 \\\\f( \frac \pi 4) = \fracCos ^2 \frac \pi 4 1+Sin ^2 \frac \pi 4 = \frac( \frac1 \sqrt2 ) ^2 1+( \frac1 \sqrt2 ) ^2 = \frac \frac12 \frac32 = \frac13\\\\f'( \frac \pi 4) = \frac-4*Cos \frac \pi 4 Sin \frac \pi 4 (1+Sin ^2 \frac \pi 4) ^2 = [/tex]