"If "y=x^(cos)+(cosx)^(x)", prove that "...

`"If "y=x^(cos)+(cosx)^(x)", prove that "(dy)/(dx)=x^(cosx).{(cosx)/(x)-(sinx)logx}+(cosx)^(x)[(log cos x)-x tan x].`

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RS AGGARWAL-DIFFERENTIATION-Exercise 10F

If (x^(x)+y^(x))=1," show that "(dy)/(dx)=-{(x^(x)(1+logx)+y^(x)(logy)...
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If y=e^(sinx)+(tanx)^(x)," prove that "(dy)/(dx)=e^(sinx)cosx+(tanx)^(...
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If y=log[x+sqrt((1+x^2)]], prove that sqrt((1+x^2)) (dy)/(dx)=1.
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"If "y=logsinsqrt(x^(2)+1)," prove that "(dy)/(dx)=(x cotsqrt(x^(2)+1)...
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"If "y=logsqrt((1-cosx)/(1+cosx))", show that "(dy)/(dx)="cosec x".
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If y=logtan(pi/4+x/2),\ show that (dy)/(dx)=secxdot Also find the ...
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is y=sqrt((1-sin2x)/(1+sin2x)), show that (dy)/(dx)+sec^2(pi/4-x)=0
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"If "y=logsqrt((1+cos^(2)x)/(1-e^(2x)))", show that "(dy)/(dx)=(e^(2x)...
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"If "y=(x)^(cosx)+(sinx)^(tanx)", prove that "(dy)/(dx)=x^(cosx){(cosx...
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"If "y=(sinx)^(cosx)+(cosx)^(sinx)", prove that "(dy)/(dx)=(sinx)^(cos...
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"If "y=(tanx)^(cotx)+(cotx)^(tanx)",prove that "(dy)/(dx)=(tanx)^(cotx...
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"If "y=x^(cos)+(cosx)^(x)", prove that "(dy)/(dx)=x^(cosx).{(cosx)/(x)...
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If y=x^(logx)+(logx)^x then find (dy)/(dx)
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"If "y=x^((x^(2)-3))+(x-3)^(x^(2))", find "(dy)/(dx).
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If f(x) =((3+x)/(1+x))^(2+3x), find f'(0)
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"If "y=(sinx)^(x)+sin^(-1)sqrtx", find "(dy)/(dx).
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If (x^2+y^2)^2=x y , find (dy)/(dx)
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If y=x^(cotx)+(2x^(2)-3)/(x^(2)+x+2), find (dy)/(dx).
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If y=tan^(-1)(a/x)+logsqrt((x-a)/(x+a)) , Prove that (dy)/(dx)=(2a^3)/...
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If x^m y^n=(x+y)^(m+n),p rov et h a t(dy)/(dx)=y/xdot
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