#### Question

# How to differentiate (a)y=x+lnx (b) y=xlnx.?

Please explain.

#### Answers

a) y = x + lnx

b) y = xlnx

So general rules you must remember for differentiation is that the

derivative of x is 1

derivative of lnx is 1/x

a) y' = 1 + 1/x

Now with b) you have xlnx so you can use the product rule, uv = uv' + vu'

let's say u = x and v = lnx so we have that u' = 1 and v' = 1/x from part a)

so uv = x times 1/x + lnx times 1 = 1 + lnx

b) y' = 1 + lnx

#1

y' = 1 + 1/x

y' = lnx + 1

#2

y' = 1 + 1/x for part a

y' = 1 + ln(x) for part b

#3

differentiate with what

if your question is differentiate y with respect to x

(a)1 + 1/x

(b)lnx + 1

#4

a) 1 +(1/x) derivative of x=1 derivative of ln(x)==1/x.....memorization

b)x(1/x)+ln(x)*1.....Product rule

simplified=====1+ln(x)

#5