What method should I use to differentiate equations with an x as the power of a number. E.g. 2^x

Take the log of both sidesln(y) = ln(2^x)This can be re-written as:ln(y) = ln(2)*xTake the exponent of both sidese^ln(y) = e^(ln(2)*x)Which gives:y = e^(ln(2)*x)Since ln(2) is a constant, apply the usual method when differentiating e^nxdy/dx = ln(2)*e^(ln(2)*x)From the question y=2^x which we re-wrote as e^(ln(2)*x) so substitute in giving he final answer:dy/dx = ln(2)*2^x

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Answered by Billy T. Maths tutor

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