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Find dy/dx if f(x) = (x + 2)^7x.

Find dy/dx if f(x) = (x + 2)^7x.-example-1
User Theabraham
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(\mathrm d)/(\mathrm dx)(x+2)^(7x)=(\mathrm d)/(\mathrm dx)e^(7x\ln(x+2))

By the chain rule, the derivative reduces to


e^(7x\ln(x+2))(\mathrm d)/(\mathrm dx)(7x\ln(x+2))=(x+2)^(7x)(\mathrm d)/(\mathrm dx)(7x\ln(x+2))

Then using the product rule, we get


(x+2)^(7x)\left(7\ln(x+2)+(7x)/(x+2)\right)
User Elethan
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