Вычисление производных функций

1. $$f(x)=(6x^7+5x)(4x^2-3x-9)$$ $$f'(x) = (42x^6+5)(4x^2-3x-9) + (6x^7+5x)(8x-3)$$
2. $$f(x)=(6\sqrt{x}+5)(x^2 - 3\frac{1}{x} - 7)$$ $$f(x) = (6x^{1/2}+5)(x^2 - \frac{3}{x} - 7)$$ $$f'(x) = (3x^{-1/2})(x^2 - \frac{3}{x} - 7) + (6x^{1/2}+5)(2x + \frac{3}{x^2})$$
3. $$f(x)=(x^4+x^3)(x^2+5x+4)$$ $$f'(x) = (4x^3+3x^2)(x^2+5x+4) + (x^4+x^3)(2x+5)$$
4. $$f(x)=(x^6+8)(x^9+x)$$ $$f'(x) = (6x^5)(x^9+x) + (x^6+8)(9x^8+1)$$
5. $$f(x)=(7\sqrt{x}+3)(\frac{8}{x}+x)$$ $$f(x)=(7x^{1/2}+3)(8x^{-1}+x)$$ $$f'(x) = (\frac{7}{2}x^{-1/2})(8x^{-1}+x) + (7x^{1/2}+3)(-8x^{-2}+1)$$
6. $$f(x)=\frac{9x^5+10}{x^7}$$ $$f'(x) = \frac{(45x^4)(x^7) - (9x^5+10)(7x^6)}{(x^7)^2}$$ $$f'(x) = \frac{45x^{11} - 63x^{11} - 70x^6}{x^{14}}$$ $$f'(x) = \frac{-18x^{11} - 70x^6}{x^{14}}$$ $$f'(x) = \frac{-18x^5 - 70}{x^8}$$
7. $$f(x)=\frac{x+\sqrt{x}}{x-5}$$ $$f(x)=\frac{x+x^{\frac{1}{2}}}{x-5}$$ $$f'(x) = \frac{(1+\frac{1}{2}x^{-1/2})(x-5) - (x+\sqrt{x})(1)}{(x-5)^2}$$
8. $$f(x)=\frac{x^4+3\sqrt{x}}{(x+6)^2}$$ $$f(x)=\frac{x^4+3x^{\frac{1}{2}}}{(x+6)^2}$$ $$f'(x) = \frac{(4x^3+\frac{3}{2}x^{-1/2})(x+6)^2 - (x^4+3\sqrt{x})(2(x+6))}{(x+6)^4}$$
9. $$f(x)=\frac{8x^2+3x}{(x^7-9)^2}$$ $$f'(x) = \frac{(16x+3)(x^7-9)^2 - (8x^2+3x)(2(x^7-9)(7x^6))}{(x^7-9)^4}$$
10. $$f(x)=\frac{7\sin x}{x^5}$$ $$f'(x) = \frac{(7\cos x)(x^5) - (7\sin x)(5x^4)}{(x^5)^2}$$ $$f'(x) = \frac{7x^5\cos x - 35x^4\sin x}{x^{10}}$$ $$f'(x) = \frac{7x\cos x - 35\sin x}{x^6}$$