# How do you use the chain rule to differentiate #y=5tan^5(2x+1)#?

##### 1 Answer

# dy/dx = 50(2x+1)^4sec^2(2x+1) #

#### Explanation:

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

If

# y=f(x) # then# f'(x)=dy/dx=dy/(du)(du)/dx #

I was taught to remember that the differential can be treated like a fraction and that the "

# dy/dx = dy/(dv)(dv)/(du)(du)/dx # etc, or# (dy/dx = dy/color(red)cancel(dv)color(red)cancel(dv)/color(blue)cancel(du)color(blue)cancel(du)/dx) # etc

So with

Using

# dy/dx = (5)(5u^4)(sec^2u)(2) #

# :. dy/dx = 50u^4sec^2u #

# :. dy/dx = 50(2x+1)^4sec^2(2x+1) #