Find the derivative of f(x) = sin(x2)

The correct option is 2xcos(x²).

To find the derivative of the function $f\left(x\right)=sin\left(x^2\right)$, we need to use the Chain Rule of calculus. The Chain Rule is used when differentiating a composite function, which is a function inside another function.

Let's define the outer and inner functions:
- The outer function is $g\left(u\right)=sin\left(u\right)$, where $u=x^2$ is the inner function.
- The inner function is $u\left(x\right)=x^2$.

According to the Chain Rule, the derivative of $f\left(x\right)=g\left(u\right(x\left)\right)$ is given by:
$$f^{\text{'}}\left(x\right)=g^{\text{'}}\left(u\right)·\frac{du}{dx}$$

Step 1: Differentiate the outer function with respect to its argument $u$:
$$\frac{d}{du}[sin(u\left)\right]=cos\left(u\right)$$

Step 2: Differentiate the inner function with respect to $x$ using the power rule:
$$\frac{d}{dx}\left[x^2\right]=2x$$

Step 3: Multiply the two derivatives together and substitute $u=x^2$ back into the equation:
$$f^{\text{'}}\left(x\right)=cos\left(x^2\right)·2x$$

Rearranging the terms, we get:
$$f^{\text{'}}\left(x\right)=2xcos\left(x^2\right)$$