how do you find the derivative of (X^2(2+x^1/2))/x^4.

Question

I'm confused because of the exponents rules. please show me the steps in simplifying the exponents then taking the derivative.

Answer 1

First lets break it up into terms that can be differentiated separately.

(x^2(2+x^1/2))/x^4
=[2x^2 + x^(5/2)]/x^4
= 2x^-2 + x^(-3/2)
Now use the x^n exponent derivative rule

df/dx = -4x^-3 -(3/2)x^(-5/2)

Answer 2

funny numbers