how to differntiate 2^x

As part of my fp1 prep, I found a question where as part of it I had to find f '(x)
where f(x) = 2^x +7x - 4

How do I find f '(x) I can differntiate the first bit =[

Reply 1

nota bene

log it?

Reply 2

silent ninja

y= 2^x

ln both sides then differentiate implicitly. See how you go.

Reply 3

kexy

dy/dx = xln2/lny ?

Reply 4

silent ninja

differentiating lny with respect to x,

d/dx[lny] = 1/y.dy/dx

Reply 5

James

y=2^x
lny = x ln2

Differentiate:
1/y y' = ln2

So y' = y ln2 = 2^x ln2

Reply 6

kexy

But I can't have any y values in it, because it's for the newton raphson process, where I sub in an X value, but no Y value :frown:

Reply 7

silent ninja

you sub back in y= 2^x at the end to get rid of the y's

Reply 8

kexy

ah clever, I like it, thanks, so i'd go

y=2^x
lny = ln2^x
lny=xln2
dy/dx (1/y) = x
dy/dx = x.2x

?

Reply 9

kexy

jamesgurung

y=2^x
lny = x ln2

Differentiate:
1/y y' = ln2

So y' = y ln2 = 2^x ln2

ah, got it, cheers, had a stupid moment there!

I'm just panicking about FP1 tommorow :frown:

Reply 10

henryt

porter2002

ah clever, I like it, thanks, so i'd go

y=2^x
lny = ln2^x
lny=xln2
dy/dx (1/y) = x
dy/dx = x.2x

?

What happened here?! It was all going so well...

Reply 11

James

porter2002

I'm just panicking about FP1 tommorow :frown:

I was going to say "I'll be up for a while so feel free to ask any questions", but on second thoughts... go to sleep!

Good luck with your exam :smile: