can anyone help me with this question? thankyou in advance and im so happy if you can show me the proper calculation ;p

Question

find dy/dx of the following functions

1. y= ( 2x^5+3x^3 -2) over x^2
2. y= (x^2+x-3) over (x^2+1)

Answer 1

I will do the second one. Use the quotient rule: d/dx (u(x)/v(x)) = (vdu/dx-udv/dx)/v²

Her du/dx = 2x + -3x^-2 and dv/dx = 2x

The derivative of the quotient is (x²+1)(2x-3x^-2) - (x²+x^-3)(2x))/(x²+1)²

You can multiply it all out if you want... or you can use Wolfram alpha calculator and type derivative of... (good place to check answers)