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