Question

Find the slope of the tangent to the curve $y=2\sqrt{x}$ at the point $(1,2)$.

Answer 1

$y=2\sqrt{x}$

$\frac{dy}{dx}=2.\frac{1}{2\sqrt{x}}=\frac{1}{\sqrt{x}}$

$\frac{dy}{dx}$ is called the slope of the tangent to the curve $y=2\sqrt{x}$ at the point $(x,y)$.
For the point $x=1$ and $y=2$, putting $x=1$ and $y=2$ in the equation $\frac{dy}{dx}=\frac{1}{\sqrt{x}}$ , we get $\frac{dy}{dx}=\frac{1}{\sqrt{1}}=1$.

Hence slope is 1.