# OPMT 5701
# 
# Homework 6b: Derivatives of ln(x) and exp(x);
# 
# Question 1
# 
> y:=ln(2*x^2-3);
> dy:=diff(y,x);
# Question 2
> y:=ln(sqrt((x-1)/(x+1)));
> dy:=diff(y,x);
> simplify(%);
# Question 3
> y:=ln(((x^2+5)^5)*((3-4*x)^4));
# Also write the function after applying the "rules" of Logathrims
> y1:=5*ln(x^2+5)+4*ln(3-4*x);
> dy:=diff(y,x);
> simplify(%);
> dy1:=diff(y1,x);
# check to see if the two versions are the same
> is(dy=dy1);
# Question 4
> y:=x^3*ln(4*x+5);
> dy:=diff(y,x);
# Question 5: find y' for y := ln(x)/ln(x^2);
# This is one that maple has a problem with.
# 
> y:=(ln(x)/ln(x^2));
> dy:=diff(y,x);
> simplify(%);
> is(dy=0);
# Now try entering the function after applying the "rules" of log
> y1:=ln(x)/(2*ln(x));
# Question 6:
# 
> y:=ln(sqrt(x^3+3*x-1)/sqrt(x^2+2*x-1));
> dy:=diff(y,x);
> simplify(%);
# Now try entering the function after applying the "rules"
> y1:=(1/2)*ln(x^3+3*x-1)-(1/2)*ln(x^2+3*x-1);
> dy1:=diff(y,x);
> simplify(%);
> is(dy=dy1);
# Question 7
> y:=exp(ln(x^2));
> dy:=diff(y,x);
# Question 8
> y:=x^2*exp(3*x);
> dy:=diff(y,x);
> factor(%);
# Question 9
> y:=(-3)*exp(4*x^4-5*x+3);
> dy:=diff(y,x);
# Question 10
> y:=(x*exp(x))/(x+1);
> dy:=diff(y,x);
> factor(%);
>