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What is the derivative of #2^x#?

Answer 1

Christopher Allers

#2^xln2#

let #y=2^x#

Take ln ( natural log) of both sides.

#rArrlny=ln2^x=xln2#

differentiate #color(blue)"implicitly with respect to x"#

#rArr1/y.dy/dx=ln2#

#rArrdy/dx=yln2=2^xln2#

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Answer 2

Charles Anctil

The derivative of (2^x) with respect to (x) is (2^x \ln(2)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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