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varsha rao Grade: 11
        

differentiate with respect to x from the first principles:


sinx^cosx


log10 to the base 'a' where a =x^x

6 years ago

Answers : (2)

Askiitians_Expert Yagyadutt
askIITians Faculty
74 Points
										

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

6 years ago
varsha rao
29 Points
										

Can you please do it from the first principles.

6 years ago
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