Question

35 б. производную функции: 1) f(x)= x³ cos x 2)f(x)= 3)f(x)=(4x+3)³

Answer 1

$1)\; \; f(x)=x^3\cdot cosx\\\\f'(x)=(x^3)'\cdot cosx+x^3\cdot (cosx)'=3x^2\cdot cosx+x^3\cdot (-sinx)=\\\\=3x^2\cdot cosx-x^3\cdot sinx\\\\2)\; \; f(x)=\frac{x^2+3}{x}\\\\f'(x)=\frac{(x^2+3)'\cdot x-(x^2+3)\cdot x'}{x^2}=\frac{2x\cdot x-(x^2+3)\cdot 1}{x^2}=\frac{x^2-3}{x^2}\\\\3)\; \; f(x)=(4x+3)^3\\\\f'(x)=3\cdot (4x+3)^2\cdot (4x+3)'=3\cdot (4x+3)^2\cdot 4=12\cdot (4x+3)^2$