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How do you differentiate #9^x#?

Answer 1

Isabella Ackerman

#ln9*9^x#

#f(x) = 9^x#

#lnf(x) = xln9#

#1/f(x)*f'(x) = ln9# (Implicit differentiation)

#f'(x) = ln9*f(x)#

#= ln9*9^x#

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Answer 2

Charles Anctil

To differentiate (9^x), you can use the formula for differentiating exponential functions. The derivative of (a^x) with respect to (x) is (a^x \cdot \ln(a)), where (a) is a constant.

So, for (9^x), the derivative is (9^x \cdot \ln(9)).

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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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