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Question
I need help differentiating the following function please.
f(x)=(sqrt x)(sinx)+In^3(1-4x)+log5(6root(x^5))+In^2(14)
log 5 is supposed to be log base 5.
thank you so much!
I think you meant "Ln" when you wrote "In" .
f(x)=[x^(1/2)][sin(x)]+[Ln(1-4x)]^3+Log5[(x^5)^(1/6)]+[Ln(14)]^2 .
Let's decompose the big term into small term %26 find each derivative individually :
f(x)=A(x)+B(x)+C(x)+D(x) .
Now,
A(x)=[x^(1/2)][sin(x)]
A'(x)=[(1/2)x^(-1/2)][sin(x)] + [x^(1/2)][cos(x)]
B(x)=[Ln(1-4x)]^3
B'(x)=3[-4/(1-4x)][Ln(1-4x)]^2
C(x)=Log5[(x^5)^(1/6)]=(5/6)Log5(x)
C'(x)=(5/6)(1/x)[1/Ln(5)]
D(x)=[Ln(14)]^2
D'(x)=0
Alon.
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Alon Mandes
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