Compute the general solution of the differential equation y' = $\displaystyle 3^x$ by integration.
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Originally Posted by ronaldo_07 Compute the general solution of the differential equation y' = $\displaystyle 3^x$ by integration. Use this: $\displaystyle \frac{d}{dx} a^x = a^x*\ln(a)*dx$
Is that a general formulae? do you know anywhere that they have a list of these formulaes?
so is the answer $\displaystyle 3^x$$\displaystyle ln(3)$
Derivative - Wikipedia, the free encyclopedia ?
after differentiating my answer back i realised that my answer should be $\displaystyle 3^x$ x $\displaystyle \frac{1}{ln3}$ how do i get from $\displaystyle 3^xln3$ to $\displaystyle 3^x$ x $\displaystyle \frac{1}{ln3}$
Originally Posted by ronaldo_07 so is the answer $\displaystyle 3^x$$\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
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