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differentiate the following function with respect to x (cos x)^x + (sin x)^1/x

differentiate the following function with respect to x
(cos x)^x + (sin x)^1/x

Grade:12

2 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago

Y1=(cosx)x

taking log on both sides

logy1=xlogcosx

diff. using product rule with respect to x

(1/y1)dy1/dx=x.(1/cosx)(-sinx) +logcosx .1

dy1/dx=(cosx)x[-xtanx+logcosx]

y2=(sinx)1/x

taking log on both sides

logy2=1/x logsinx

diff. using product rule with respect to x

(1/y2)dy2/dx=(1/x)(1/sinx)(cosx)+logsinx(-1/x2)

dy2/dx=(sinx)1/x[(cotx)/x-(1/x2)logsinx]

hence dy/dx=(cosx)x[-xtanx+logcosx]+(sinx)1/x[(cotx)/x-(1/x2)logsinx]

Thanks & Regards

Rinkoo Gupta

AskIITians Faculty

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hello
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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