I need to find the derivative of (8x+9)^x. How do I approach that? Do I use the rule that g^x = g^x * ln (g) ?

Question

anonymous · Answer

I mean that the derivative of g^x = g^x * ln *(g)

turingtest · Answer

yes, plus the chain rule...$$f(x)=(8x+9)^x$$chain rule:$$f'(x)=(8x+9)^x \ln (8x+9)(8)=8(8x+9)^x \ln (8x+9)$$

anonymous · Answer

The homework program in which I have to turn this in says this is false sadly. As a tip it gives taking the natural logarithm before deriving..

turingtest · Answer

Yeah, sorry. Seemed straight-forward to me. I'll try the log thing but in the meantime here's Wolfram's answer: http://www.wolframalpha.com/input/?i=d%2Fdx%28%288x%2B9%29^x%29

turingtest · Answer

$$y=(8x+9)^x$$$$\ln y=x \ln (8x+9)$$differentiating implicitly with the product rule gives$$y'/y=\ln(8x+9)+8x/(8x+9)$$$$y'=y[\ln(8x+9)+8x/(8x+9)]$$$$y'=(8x+9)^x[\ln(8x+9)+8x/(8x+9)]$$there we go!

anonymous · Answer

Thank you kindly good sir, just what I was looking for.

turingtest · Answer

anytime!