Question

425.Посчитайте $f'(a)$ при:
c)$f(x)=3x*sin(x),a=\frac{\pi}{6}$

Answer 1

$f(x)=3x\cdot sinx\ \ ,\ \ a=\dfrac{\pi}{6}\\\\\\f'(x)=3\cdot sinx+3x\cdot cosx\\\\\\f'(\dfrac{\pi}{6})=3\cdot sin\dfrac{\pi}{6}+3\cdot \dfrac{\pi}{6}\cdot cos\dfrac{\pi}{6}=3\cdot \dfrac{1}{2}+\dfrac{\pi}{2}\cdot \dfrac{\sqrt3}{2}=\dfrac{6+\pi \sqrt3}{4}$