hey i got a problem with differentiation, and im not having much luck the question is if i have a exponential function y=12*0.5^x how would find y'
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Hello, Transform it with logarithms. You can't derivate correctly when there is x in the power. ln(ab)=ln(a)+ln(b) ln(a^b)=b ln(a) ;-)
okay thanks so its = ln(12) +ln(0.5^x) = ln(12) + xln(0.5) =x ln(0.5) + ln(12) =x ln(0.5 * 12) =x ln(6) = 1.79x
Originally Posted by Quill okay thanks so its = ln(12) +ln(0.5^x) = ln(12) + xln(0.5) =x ln(0.5) + ln(12) =x ln(0.5 * 12) =x ln(6) = 1.79x No. which just has the form . And you know how to differentiate that form, right? So you end up with . Capisce? A formula worth remembering.
um i think i got it y=12*0.5^x =12(0.5^x) =12(e^ln0.5^x) =12(e^xln0.5) =12(ln0.5)0.5^x thanks again
Originally Posted by Quill um i think i got it y=12*0.5^x =12(0.5^x) =12(e^ln0.5^x) =12(e^xln0.5) =12(ln0.5)0.5^x thanks again indeed. now that you know two ways to find the derivative of functions like this, it's time for the general rule. where is a constant
thanks one last thing, when i graph it, i get an almost straight line, is that normal
Originally Posted by Quill thanks one last thing, when i graph it, i get an almost straight line, is that normal It might look that way, depending on the scale you've used. But it most certainly is not a straight line.
are yer that made it work thanks
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