Home > Calculus > Differentiating Logarithmic Functions without Base e

How do you find the derivative of # log 4^(x^2)#?

Answer 1

Cameron Alexander

#d/dxlog4^(x^2)=2xlog4#

We use the following rule to simplify the function:

#loga^b=bloga#

#log4^(x^2)=x^2log4#

and

#d/dxlog4^(x^2)=d/dxx^2log4=2xlog4#

Remember that #log4# is just a constant.

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Answer 2

Charles Arocha

To find the derivative of ( \log{(4^{x^2})} ), you can use the chain rule. The derivative is ( \frac{d}{dx} \left( \log{(4^{x^2})} \right) = \frac{1}{\ln(4)} \cdot \frac{d}{dx} (x^2) = \frac{2x}{\ln(4)} ).

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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.