## Calculus Tutorial

*Composite exponential function differentiation*

#### Intro

When we differentiate the composite exponential function, we want to use the product rule and the chain rule.

#### Sample Problem

y=(ln(x))x

find dy/dx

#### Solution

y=(ln(x))x

ln(y)=ln(ln(x))x take (ln) both side

ln(y)=x(ln(ln(x)) ln(a)m=m.ln(a)

d/dx(ln(y))=d/dx(x(ln(ln(x))) take derivative both side

1/y.dy/dx=x.d/dx(ln(ln(x)))+ln(ln(x)).d/dx(x) product rule

1/y.dy/dx=x.1/ln(x).1/x+ln(ln(x)).1 chain rule

1/y.dy/dx=1/ln(x)+ln(ln(x)) simplify

dy/dx=y.(1/ln(x)+ln(ln(x))) multiply by y both side

dy/dx=ln(x)x.(1/ln(x)+ln(ln(x))) substituting y

# About The Author

Mathematics Teacher |

I was a teacher in Srilanka from 1992 to 2006. I took tuition from 1990 to 1991 in India. I do general work in Canada but I help to do homework to my daughters. I finished my teacher\'s training college diploma in Srilanka. I completed my B.Sc degree course at Bharayiar university in India. |