how do you find the derivative of (X^2(2+x^1/2))/x^4.
I'm confused because of the exponents rules. please show me the steps in simplifying the exponents then taking the derivative.
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)