y
=
a^x，
rule
x
=
Log (a,
y)，
therefore
x'(y)
=
1/yln(a)，
but
y
=
a^x
and
x
=
Log (a,
y)
Is the inverse function,
therefore
x'(y)
*
y'(x)
=
1,
therefore
y'(x)
=
yln(a)
=
a^x*ln(a).
In particular,
while
a
=
e
Sometimes.
y
=
e^x，
hello
=
e^x.
Generally, the inverse function is used to solve the derivative of the index. If you understand it, you can also try to solve the derivative of F(X)=X to the x power.