Найдите производную функции: а) (x^3+3) * (x-x^3) ; б) x^4 - x^2/x-1

A) f (x) = 3x-4x 3 x 0 =5 f ′ (x) = 3-12x 2 f ′ (x 0 ) = 3-12 (5) 2 =-297

/begin{lgathered}b) f (x) = x^7-3x^6+3x^3-23; / x_0=-1 / / f' (x) = 7x^6-18x^5+9x^2 / / f' (x_0) = 7+18+9=34/end{lgathered} b) f (x) = x 7 -3x 6 +3x 3 -23; x 0 =-1 f ′ (x) = 7x 6 -18x 5 +9x 2 f ′ (x 0 ) = 7+18+9=34

/begin{lgathered}c) f (x) (1+2x) (2x-1) + 4x^2; / x_0=0,5 / / f' (x) = (1+2x) * 2+2 (2x-1) + 8x / / f' (x_0) = (1+2*0,5) * 2+2 * (2*0,5-1) + 8*0,5 = / / = 4+0+4=8/end{lgathered} c) f (x) (1+2x) (2x-1) + 4x 2 ; x 0 =0,5 f ′ (x) = (1+2x) ∗2+2 (2x-1) + 8x f ′ (x 0 ) = (1+2∗0,5) ∗2+2∗ (2∗0,5-1) + 8∗0,5= =4+0+4=8

/begin{lgathered}d) f (x) = x^2 (x-5) ; / x_0=-4 / / f' (x) = 2x (x-5) + x^2*1 / / f' (x_0) = - 8 (-4-5) + 16=88/end{lgathered} d) f (x) = x 2 (x-5) ; x 0 =-4 f ′ (x) = 2x (x-5) + x 2 ∗1 f ′ (x 0 ) = - 8 (-4-5) + 16=8