# Maths Implicit differneiation

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#1
why does y= a^x differentiate to a^xlna

i dont get the logic behind it
0
5 years ago
#2
ln(a) is a constant

Differentiate 9x you get 9
1
5 years ago
#3
(Original post by brainmatter)
why does y= a^x differentiate to a^xlna

i dont get the logic behind it
Take logs of both sides:

0
5 years ago
#4
0
#5
Take logs of both sides:

how is this taking logs of both sides, wouldn't it be a on RHS if logs of both sides was taken?
0
5 years ago
#6
(Original post by brainmatter)
how is this taking logs of both sides, wouldn't it be a on RHS if logs of both sides was taken?
Apply the log function to both sides. log(y) = log(x^a)

Bring down the exponent, using the property of logs, on the RHS to get log(y) = alog(x)
0
5 years ago
#7
You could also write a^x = e^(xlna)

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