Question

What is the derivative of `sqrtx/(x^4)`?

Answer 1

`-7/2x^(-9/2)` or `-3.5x^-4.5`

Explanation:

We're taking the derivative of a quotient. Quotient Rule, right? Well you could go through all of that trouble, but pay close attention to the expression we're taking the derivative of:

`sqrtx/(x^4)`

We can rewrite `sqrtx` as `x^(1/2)`, which now gives us

`(x^(1/2))/x^4`

Since we have the same bases, we can subtract the exponents to get

`x^(-7/2)`

Now this is something we can easily take the derivative of! With the power rule, the exponent is brought out front, and the power is decremented by one. We now have

`-7/2x^(-9/2)` or `-3.5x^-4.5`

So we avoided the quotient rule by just paying close attention to the expression.

Hope this helps!