# [SOLVED] Differential

• Feb 16th 2009, 10:27 AM
ronaldo_07
[SOLVED] Differential
Compute the general solution of the differential equation y' = $\displaystyle 3^x$ by integration.
• Feb 16th 2009, 10:41 AM
Jameson
Quote:

Originally Posted by ronaldo_07
Compute the general solution of the differential equation y' = $\displaystyle 3^x$ by integration.

Use this: $\displaystyle \frac{d}{dx} a^x = a^x*\ln(a)*dx$
• Feb 16th 2009, 10:50 AM
ronaldo_07
Is that a general formulae? do you know anywhere that they have a list of these formulaes?
• Feb 16th 2009, 10:52 AM
ronaldo_07
so is the answer $\displaystyle 3^x$$\displaystyle ln(3) • Feb 16th 2009, 10:53 AM Jameson • Feb 16th 2009, 11:07 AM ronaldo_07 after differentiating my answer back i realised that my answer should be \displaystyle 3^x x \displaystyle \frac{1}{ln3} how do i get from \displaystyle 3^xln3 to \displaystyle 3^x x \displaystyle \frac{1}{ln3} • Feb 16th 2009, 11:07 AM Jameson Quote: Originally Posted by ronaldo_07 so is the answer \displaystyle 3^x$$\displaystyle ln(3)$

$\displaystyle \frac{3^x}{\ln{3}}$. You have to divide by ln3 to compensate for when you take the derivative you will multiply by ln3