How do you differentiate y= (5x)/((tanx)(cotx))?

3 Answers
Apr 13, 2015

5

tan x * cot x is simply 1, because cot x equals 1/tan x. Thus it is y= 5x. Hence dy/dx =5

Apr 13, 2015

If you don't think first (before you start) you'll use the quotient rule (with the product rule to differentiate the denominator).

Take a few seconds to think, and to ask:
Can I rewrite this before I differentiate to make my life easier?

tanx = 1/cotx so tanx cotx =1

That means that y = 5x/1=5x

So, y'=5

Apr 13, 2015

y'=5

y=(5x)/((tanx)(cotx)

As

tanx=sinx/cosx

And

cotx=cosx/sinx

So,

y=(5x)/((sinx/cosx)(cosx/sinx))

y=(5x)/((cancelsinx/cancelcosx)(cancelcosx/cancelsinx))

y=(5x)/1

y=(5x)

Differentiating both sides with respect to 'x'

y'=5