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Differentiate f(x)=x^x + x^a +a^x +a^a ,for some fixed a>0

Differentiate f(x)=x^x + x^a +a^x +a^a ,for some fixed a>0

Grade:11

1 Answers

Abhishek Doyal
askIITians Faculty 25 Points
10 years ago
f(x)=x^x+x^a+a^x+a^a
letA(x)=x^x
take both side log
logA(x)=xlog(x)
differentiate
A'(x)/A(x)=log(x)+x.1/x=1+log(x) eq 1 so A'(x)=x^x(1+log(x))

B(x)=x^a
B'(x)=ax^(a-1) eq 2

C(x)=a^x

take both side log
logC(x)=xlog(a)
differentiate
C'(x)/C(x)=log(a)
C'(x)=a^xlog(a) eq 3


D(x)=a^a
D'(x)=0 because of constant function eq4

by eq1, eq 2,eq 3,eq 4

so f''(x)=x^x(1+log(x))+ax^(a-1)+a^xlog(a)
Abhishek doyal
IIT Bombay
Askiitian tutor


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