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How do you find the derivative of #f(x)=x^ln(3)#?

Answer 1

Evelyn Agard

ln3 #x^(ln3 -1)#

Simply apply the power rule to get the result. #d/dx x^ln3# = ln3#x^(ln3-1)#

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Answer 2

Charles Arocha

To find the derivative of ( f(x) = x^{\ln(3)} ), you can use the chain rule. The chain rule states that if you have a function ( g(x) ) inside another function ( h(x) ), then the derivative of ( h(g(x)) ) with respect to ( x ) is ( h'(g(x)) \times g'(x) ).

Applying the chain rule to ( f(x) = x^{\ln(3)} ), we have:

[ f'(x) = (\ln(3) \times x^{\ln(3)-1}) ]

So, the derivative of ( f(x) ) with respect to ( x ) is ( f'(x) = \ln(3) \times x^{\ln(3)-1} ).

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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.