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differentiate with respect to x from the first principles:
sinx^cosx
log10 to the base 'a' where a =x^x
Hiii !varsha
1) sinx ^ cosx
Let it as y = sinx ^ cos x
ln (y) = cosx . ln(sinx)
1/y .dy/dx = -sinx.ln(sinx) + cos^2(x)/sinx
dy/dx = y [ cos^2(x)/sin(x) - sin(x).ln(sinx) ]
Substitute y = sinx^cosx
2) log 10 base a = y
ln(10)/ln(a) = y
1/y = ln(a)/ln(10)
1/y = ln(x^x)/ln(10) = x.ln(x)/ln10
(-1/y^2) dy.dx = 1/ln(10) + ln(x)/10
dy/dx = -y^2 ( ln(x) + 1)/ln(10)
SUbstitute y = ln(10)/ln(x^x)
With regards
Yagya
askiitians_expert
Can you please do it from the first principles.
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