Question

Найдите производную функции 1) f(x)=cos x (5-x^2)
2) f(x)=(x+2)/sin x
3)f(x)=(5x^2-1)* (x+4)
4) f(x)=(3x^5-2)^8
5) f(x)=cos 5x

Answer 1

1)f'(x)=-sinx(5-x²)+cosx*(-2x)=-sinx(5-x²)-2xcosx

2)f'(x)= 1*sinx-(x+2)*cosx/sin²x=sinx-(x+2)cosx/sin²x

3)f'(x)=10x(x+4)-(5x²-1)/(x+4)² =10x²+40x-5x²+1/(x+4)² = 5x²+40x+1/(x+4)²

4)f'(x)= 8*(3x^5 -2)^7 * 15x^4

5)f'(x)= -sin5x * 5