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What is the derivative of 2^x?

Answer 1

Elijah Abram

#d/(dx) 2^x = 2^x*ln 2#

By the definition of natural logarithm:

#e^(ln 2) = 2#

So:

#2^x = (e^(ln 2))^x = e^(x ln 2)#

Given that:

#d/(dx) e^x = e^x#

we can use the chain rule to deduce:

#d/(dx) 2^x = d/(dx) e^(x ln 2)#

#color(white)(d/(dx) 2^x) = e^(x ln 2) * d/(dx) (x ln 2)#

#color(white)(d/(dx) 2^x) = e^(x ln 2) * ln 2#

#color(white)(d/(dx) 2^x) = 2^x * ln 2#

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Answer 2

Emily Ammerman

#2^xln2#.

we know #d/dx a^x=a^x lna#.so the ans.

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Answer 3

Scarlett Allison

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.