Find the gradient of the tangent to the curve y= square root x plus 8/square root x at the point (4,6)

y=\sqrt{x}+\frac{8}{\sqrt{x}}

Please use proper grouping so we know what you mean. I knew this by plugging in x=4 and seeing if I got 6.

To find the gradient, we need the slope at that point.

Find the derivative of y, then plug in x=4. That should be the slope at that point.

Can you find the derivative of y?

The derivative may be easier to find by rewriting as

x^{\frac{1}{2}}+8x^{\frac{-1}{2}}