Упр.872 ГДЗ Алимов 10-11 класс (Алгебра)

Применим правило производной произведения:

$$f(x)=x^2\cos x$$

$$f'(x)=(x^2)’\cos x+x^2(\cos x)’=2x\cos x-x^2\sin x$$

$$f(x)=x^3\ln x$$

$$f'(x)=(x^3)’\ln x+x^3(\ln x)’=3x^2\ln x+x^3\cdot\frac1x=3x^2\ln x+x^2$$

$$f(x)=5x e^x$$

$$f'(x)=(5x)’e^x+5x(e^x)’=5e^x+5xe^x=5e^x(1+x)$$

$$f(x)=x\sin 2x$$

$$f'(x)=(x)’\sin 2x+x(\sin 2x)’=\sin 2x+2x\cos 2x$$

$$f(x)=e^{-x}\sin x$$

$$f'(x)=(e^{-x})’\sin x+e^{-x}(\sin x)’=-e^{-x}\sin x+e^{-x}\cos x$$

$$f'(x)=e^{-x}(\cos x-\sin x)$$

$$f(x)=e^x\cos x$$

$$f'(x)=(e^x)’\cos x+e^x(\cos x)’=e^x\cos x-e^x\sin x$$

$$f'(x)=e^x(\cos x-\sin x)$$