What is the derivative of 10^x?

Answer 1
There is a rule for differentiating these functions #(d)/(dx) [a^u]=(ln a)* (a^u) * (du)/(dx)#

Notice that for our problem a=10 and u=x so let's plug in what we know.

#(d)/(dx) [10^x]=(ln 10)* (10^x)* (du)/(dx)#
if #u=x# then, #(du)/(dx)=1# because of the power rule: #(d)/(dx) [x^n]=n*x^(n-1)#
so, back to our problem, #(d)/(dx) [10^x]=(ln 10) * (10^x) * (1)#
which simplifies to #(d)/(dx) [10^x]=(ln 10) * (10^x) #

This would work the same if u was something more complicated than x. A lot of calculus deals with the ability to relate the given problem to one of the rules of differentiation. Often we have to alter the way the problem looks before we can begin, however that was not the case with this problem.

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Answer 2

The derivative of (10^x) is (10^x) multiplied by the natural logarithm of the base, which is (10). So, the derivative is (10^x \ln(10)).

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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.

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.

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.

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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