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How do you differentiate #y=2^x?

Answer 1

The answer is dy/dx[f'(x)]=2^x ln 2.

According to chain rule, differentiation of 2^x would be 2^x and the natural log of the base is multiplied to it. You can also take log on both sides and apply log rule to change base for obtaining the answer. The second method would be easier for those who have difficulty in performing chain rule.

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Answer 2

Samantha Adkison

To differentiate ( y = 2^x ) with respect to ( x ), you can use the power rule of differentiation. The derivative of ( a^x ) with respect to ( x ) is ( a^x \ln(a) ). Applying this rule to ( y = 2^x ), the derivative is:

[ \frac{dy}{dx} = 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.