Question

b) Find the differential coefficient of the following
function,
3.
6
y= (x-1))³/² (x-3)½
______________
(x-2)²​

Answer 1

What is the differential coefficient of x^2/x^3+1?

Instead of the quotient rule we can approach this problem in an elegant way.

I am assuming the problem to be:

What is the differential coefficient of x2x3+1.

Now let y=x2x3+1.

Take log on both sides.

logy=log(x2)−log(x3+1)

Differentiate both sides,

1ydydx=2xx2−3x2x3+1.

The final answer is dydx=x2x3+1(2xx2−3x2x3+1