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If x^ydoty^x=1,p rov et h a t(dy)/(dx)=-...

If `x^ydoty^x=1,p rov et h a t(dy)/(dx)=-(y(y+xlogy)/(x(ylogx+x)`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y=(xsin^(-1)x)/(sqrt(1-x^2)),"p r o v et h a t"(1-x^2)(dy)/(dx)=x+...

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  2. Differentiate the following function tan^2x

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  3. If x^ydoty^x=1,p rov et h a t(dy)/(dx)=-(y(y+xlogy)/(x(ylogx+x)

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  4. If x y^2=1,p rov et h a t2(dy)/(dx)+y^3=0

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  5. Find (dy)/(dx) in each of the following: e^(x-y)=log(x/y)

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  6. Find (dy)/(dx) in each of the following: sinx y+cos(x+y)=1

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  7. If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y), prove that (dy)/(dx)=sqrt((1-y^2)/(...

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

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  9. Differentiate the following function with respect to x : cos^-1s...

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  10. Differentiate the following function with respect to x : cos^(-1){...

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  11. If sec((x+y)/(x-y))=a , prove that (dy)/(dx)=y/x .

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  12. Differentiate the following function with respect to x : sin^(-1...

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  13. Differentiate the following function with respect to x : tan^(-1...

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  14. If x=sin^(-1)[(2t)/(1+t^2)]'and'y=tan^(-1)((2t)/(1-t^2)), prove that d...

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  15. If x^(13)y^7=(x+y)^(20),p rov et h a t(dy)/(dx)=y/xdot

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  16. Find (dy)/(dx), when x=cos^(-1)1/(sqrt(1+t^2))"and"y=sin^(-1)1/(sqrt(1...

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  17. If x=2costheta-cos2theta"and"y=2sintheta-sin2theta" Prove that" (dy)/...

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  18. If x=cost " and " y=sint ,"prove : "(dy)/(dx)=1/(sqrt(3))"at " t=(2pi)...

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  19. Differentiate the following functions with respect to cos(logx)hat2

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  20. Differentiate the following functions with respect to e^(a x)secxta...

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