Question

How do you find the derivative of `(6x*sqrtx)+(8/(x^2*sqrtx))`?

Answer 1

`9sqrt(x) - 20/(x^3 * sqrt(x))`

Explanation:

Change the function into a more workable form with laws of indices. Problems like these are often written to look incomprehensible but become straightforward when rearranged.

`6x^(3/2) + 8x^(-5/2)`

Now differentiate in the normal fashion.

`9x^(1/2) - 20x^(-7/2)`
`= 9sqrt(x) - 20/(x^3 * sqrt(x))`