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(sinx-cosx)^((sinx-cosx)),(pi)/(4) ltx l...

`(sinx-cosx)^((sinx-cosx)),(pi)/(4) ltx lt (3pi)/(4)`

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Let `y=(sinx-cosx)(sinx-cosx)`
`implieslogy=log(sinx-cosx)^((sinx-cosx))`
`=(sinx-cosx)log(sinx-cosx)`
Differentiate both sides w.r.t. x
`(1)/(y)(dy)/(dx)=(sin x-cos x)(d)/(dx)log(sinx-cosx)+log(sinx-cosx)(d)/(dx)(sinx-cosx)`
`implies(dy)/(dx)=[((sin x-cos x))/(sinx-cosx)*(d)/(dx)(sinx-cosx)+log(sinx-cosx)*(cosx+sinx)]`
`=y[(cosx+sinx)+(cosx+sinx)log(sinx-cosx)]`
`=(sinx-cosx)^((sinx-cosx))(cosx+sinx)[1+log(sinx-cosx)]`
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NAGEEN PRAKASHAN-Continuity and Differentiability-Miscellaneous Exercise
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  4. (log x)^(log x),x gt1

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  5. Differentiate w.r.t. x the function cos" "(a" "cos" "x" "+" "b" "s in"...

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  6. (sinx-cosx)^((sinx-cosx)),(pi)/(4) ltx lt (3pi)/(4)

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  8. Differentiate x^x^(2-3)+(x-3)^x^2 with respect to x :

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  9. Find (dy)/(dx),if y=12(1-cost), x=10(t-sint),-pi/2<t<pi/2

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  10. If y=sin^(- 1)x+sin^(- 1)sqrt(1-x^2) then find (dy)/(dx)

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  11. "If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).

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  12. If (x-a)^2+(y-b)^2=c^2, for some c > 0, prove that ([1+((dy)/(dx))^2]^...

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  13. If cosy=xcos(a+y), with cosa!=+-1, prove that (dy)/(dx)=(cos^2(a+y...

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  14. If x=a(cost+tsint) and y=a(sint-tcost), find (d^(2)y)/(dx^(2)).

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  15. If f(x)=|x|^3 , show that f"(x) exists for all real x and find it.

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