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What is the derivative of #f(x)=e^(4x)*log(1-x)# ?

Answer 1

Paisley Johnson

#f'(x)=e^(4x)/ln10(4ln(1-x)-1/(1-x))#

Explanation :

#f(x)=e^(4x)⋅log(1−x)#

Converting from base #10# to #e#

#f(x)=e^(4x)⋅ln(1−x)/ln10#

Using Product Rule, which is

#y=f(x)*g(x)#

#y'=f(x)*g'(x)+f'(x)*g(x)#

Similarly following for the given problem,

#f'(x)=e^(4x)/ln10*1/(1-x)(-1)+ln(1−x)/ln10*e^(4x)*(4)#

#f'(x)=e^(4x)/ln10(4ln(1-x)-1/(1-x))#

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Answer 2

Aurora Alvarado

To find the derivative of ( f(x) = e^{4x} \cdot \log(1-x) ), you can use the product rule. The derivative is:

[ f'(x) = e^{4x} \cdot \frac{d}{dx}[\log(1-x)] + \frac{d}{dx}[e^{4x}] \cdot \log(1-x) ]

[ f'(x) = e^{4x} \cdot \left(\frac{1}{1-x}\right) \cdot (-1) + 4e^{4x} \cdot \log(1-x) ]

[ f'(x) = -\frac{e^{4x}}{1-x} + 4e^{4x} \cdot \log(1-x) ]

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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.