Find slope of tangent line

Question

Find slope of the tangent line $$g(x)={5\over \sqrt{x}}$$ at x=9

Answer 1

Hint $$\frac{d}{dx} \sqrt{x} = \frac{1}{2\sqrt{x}}$$

Answer 2

Just simply differentiate your function $g(x)$: $$g(x)=5x^{-1/2}$$ Now, use the fact that: $$\frac{d}{dx} (x^n)=nx^{n-1}$$ To obtain an expression for $g'(x)$ and then find $g'(9)$ (substitute $x=9$) to give you the slope.