Question

Differentiation:
If f(x)=9sinx + sin3x,
Find f'(π\3)​

Answer 1

Answer:

$\frac{3}{2}$

Step-by-step explanation:

$f(x) = 9sinx +sin 3x$

Now it is known that differential of sin(x) is:

$\frac{d}{dx}sinax = a.cosx$

So,

$f'(x) = 9\frac{d}{dx}sinx +\frac{d}{dx}sin3x\\=9.cosx +3.cos3x$

Now put value of x as π/3

$f'(\frac{\pi}{3}) = 9cos(\frac{\pi}{3}) + 3cos(3.\frac{\pi}{3})\\=\frac{9}{2} + 3(-1) =\frac{3}{2}$

Answer 2

Solution in attachment