Differentiate f(x)=x^x + x^a +a^x +a^a ,for some fixed a>0
AnupamDavidSamrat , 11 Years ago
Grade 11
Differential Calculus> differentiate...
1 Answers
Abhishek Doyal
Last Activity: 11 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
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