Question

Найдите производную а) y=cos (x^10+3) б) y=√sin x-2 в) y=sin^42x+cos^35x

Answer 1

А) $\mathtt{f'(x)=[cos(x^{10}+3)]'=-sin(x^{10}+3)(x^{10}+3)'=-10x^9sin(x^{10}+3)}$

б) $\mathtt{f'(x)=(\sqrt{sinx-2})'=\frac{1}{2\sqrt{sinx-2}}*(sinx-2)'=\frac{cosx}{2\sqrt{sinx-2}}}$

в) 

$\mathtt{f'(x)=(sin^42x+cos^35x)'=(sin^42x)'+(cos^35x)'=}\\\mathtt{4sin^32x(sin2x)'+3cos^25x(cos5x)'=}\\\mathtt{4sin^32x*cos2x(2x)'-3cos^25x*sin5x(5x)'=}\\\mathtt{8sin^32x*cos2x-15cos^25x*sin5x=}\\\mathtt{4sin^22x*sin4x-\frac{15}{2}cos5x*sin10x}$