see a^a is constant hence it's differentiation =0 so y=x^x +a^a let it y=x^x take log logy=xlogx differentiate (1/y)(dy/dx)=logx+x(1/x)::::::::::(1) dy/dx=y(logx+1) dy/dx=(x^x+a^a)(logx+1)
let m=x^x dm/dx=x^x(1+logx)....(from(1)) let n=a^x logn=xloga (1/n)(dn/dx)=loga dn/dx=a^x(loga),,,,,,(2) let p =x^a dp/dx=ax^(a-1).....(3) let r=a^a dr/dx=0......(4) Now question becomes y=m+n+p+r differentiate dy/dx=dm/dx + dn/dx +dp/dx +dr/dx put the value from (1)(2)(3)(4) dy/dx=x^x(1+logx)+a^x(loga)+ax^(a-1)+0
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YASH3100
Brother for the 1st one even I got the same answer but the answer is given to be x^x(1+logx)
Answers & Comments
see a^a is constant hence it's differentiation =0
so
y=x^x +a^a
let it
y=x^x
take log
logy=xlogx
differentiate
(1/y)(dy/dx)=logx+x(1/x)::::::::::(1)
dy/dx=y(logx+1)
dy/dx=(x^x+a^a)(logx+1)
let m=x^x
dm/dx=x^x(1+logx)....(from(1))
let n=a^x
logn=xloga
(1/n)(dn/dx)=loga
dn/dx=a^x(loga),,,,,,(2)
let p =x^a
dp/dx=ax^(a-1).....(3)
let r=a^a
dr/dx=0......(4)
Now question becomes
y=m+n+p+r
differentiate
dy/dx=dm/dx + dn/dx +dp/dx +dr/dx
put the value from (1)(2)(3)(4)
dy/dx=x^x(1+logx)+a^x(loga)+ax^(a-1)+0