# What is the derivative of this function #y= (1+sin x)/(1-sin x)#?

##### 1 Answer

Nov 5, 2016

#### Explanation:

If you are studying maths, then you should learn the Quotient Rule for Differentiation, and practice how to use it:

# d/dx(u/v) = (v(du)/dx-u(dv)/dx)/v^2 # , or less formally,# (u/v)' = (v(du)-u(dv))/v^2 #

I was taught to remember the rule in word; " *vdu minus udv all over v squared* ". To help with the ordering I was taught to remember the acronym, VDU as in Visual Display Unit.

So with

# :. d/dx(u/v) = (v(du)/dx-u(dv)/dx)/v^2 #

# :. dy/dx = ( (1-sinx)(cosx) - (1+sinx)(-cosx) ) / (1-sinx)^2#

# :. dy/dx = ( cosx-sinxcosx + cosx +sinxcosx ) / (1-sinx)^2#

# :. dy/dx = ( 2cosx ) / (1-sinx)^2#