Упр.179 ГДЗ Колягин Ткачёва 11 класс (Алгебра)

179. Найти производную функции: 1) $$x^6$$; 2) $$x^{12}$$; 3) $$3x^4+2x^{13}$$; 4) $$7x^3-3x^7$$; 5) $$\frac{3}{x^4}$$; 6) $$x^3+\frac{1}{x^2}$$.

1. $$f(x)=x^6$$
   $$f'(x)=6x^5$$
2. $$f(x)=x^{12}$$
   $$f'(x)=12x^{11}$$
3. $$f(x)=3x^4+2x^{13}$$
   $$f'(x)=3\cdot 4x^3+2\cdot 13x^{12}=12x^3+26x^{12}$$
4. $$f(x)=7x^3-3x^7$$
   $$f'(x)=7\cdot 3x^2-3\cdot 7x^6=21x^2-21x^6$$
5. $$f(x)=\frac{3}{x^4}=3x^{-4}$$
   $$f'(x)=3\cdot(-4)x^{-5}=-12x^{-5}=-\frac{12}{x^5}$$
6. $$f(x)=x^3+\frac{1}{x^2}=x^3+x^{-2}$$
   $$f'(x)=3x^2-2x^{-3}=3x^2-\frac{2}{x^3}$$

Ответ

1. $$f'(x)=6x^5$$
2. $$f'(x)=12x^{11}$$
3. $$f'(x)=12x^3+26x^{12}$$
4. $$f'(x)=21x^2-21x^6$$
5. $$f'(x)=-\frac{12}{x^5}$$
6. $$f'(x)=3x^2-\frac{2}{x^3}$$