Question

F(x)=sinx,x0=p/3 производная

Answer 1

Берём производную:
f(x)'=(sinx)'=cosx=cosП/3=cos60°=1/2

Answer 2

To find the derivative of the function $F(x) = \sin x$ at the point $x_0 = \frac{\pi}{3}$, we'll use the rules of differentiation. The derivative of $\sin x$ with respect to $x$ is $\cos x$.

So, the derivative of $F(x) = \sin x$ is:

$F'(x) = \cos x$

Now, to find the derivative at $x_0 = \frac{\pi}{3}$, we simply substitute $x_0$ into the derivative:

$F'\left(\frac{\pi}{3}\right) = \cos\left(\frac{\pi}{3}\right)$

The value of $\cos\left(\frac{\pi}{3}\right)$ can be evaluated as follows:

$\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}$

So, the derivative of $F(x) = \sin x$ at $x_0 = \frac{\pi}{3}$ is:

$F'\left(\frac{\pi}{3}\right) = \frac{1}{2}$