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How do you find the derivative of #8^(2x)#?

Answer 1

Ezra Adams

#d/dx8^(2x)=8^(2x)*2ln8#

Applying the rule #d/dxa^(u(x))=a^u*lna*(du)/dx#, to this question we get

#d/dx8^(2x)=8^(2x)*ln8*2#

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Answer 2

Cameron Alexander

To find the derivative of (8^{2x}), you can use the chain rule. First, take the natural logarithm of the function to simplify it. Then differentiate with respect to (x), and finally multiply by the derivative of the exponent. The derivative is:

[ \frac{d}{dx} (8^{2x}) = \frac{d}{dx} (e^{2x \ln(8)}) = \frac{d}{dx} (e^{2x \ln(8)}) = 2\ln(8) \cdot 8^{2x} ]

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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.