Exponential function question (1 Viewer)

[Mr Lovepony]

Just finished 2U maths exams but couldn't do this one:

Find the primitive function of 4 to the power of x.

Help would be much appreciated.

 

[word.]

take note that 4 = e^ln4

 

[rama_v]

Going on from what word said

y = 4^x = e^{ln 4x}= e^{xln 4}


Int(y dx) = (1/ln 4) e^{xln 4} + C
= (1/ln 4) 4^x + C

 

[Riviet]

In general:

d/dx(a^x)=a^x.log_ea

The integral of a^x is also useful to know:

∫a^xdx = a^x/log_ea + C

 

[Mr Lovepony]

Hmm, thanks. It's something that I've never encountered before.

 

[nadinetannous]

wow- we didn't learn that in maths.

 

[rama_v]

wow- we didn't learn that in maths.

You probably will encounter it later then in any case... It pops up every now and then