Derivative of the Sine Function

Question

Consider the function $$g(x)=\sin(x)$$ as shown in the graph below. All of the following statements about its derivative are true except:

Accepted Answer

At $$x=\frac{\pi}{2}$$, the derivative equals the function value, meaning $$g'(\frac{\pi}{2})=g(\frac{\pi}{2})$$.

Answer

The derivative of $$\sin(x)$$ is $$\cos(x)$$.

Answer

At any point where the tangent is horizontal, the derivative is zero.

Answer

The derivative of $$g(x)$$ represents the slope of the tangent line at any given point.