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Differentiate log sinx from first princ...

Differentiate log `sinx` from first principle.

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate the following functions with respect to x : (x^2+x+1)^...

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  2. Differentiate the following functions with respect to x : (i)logsinx^...

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  3. Differentiate log sinx from first principle.

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  4. If f(x)=|logx|,xgt0,find f^(prime)(1/e)a n df^(prime)(e)

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  5. Differentiate sin^(-1)sqrt(x)(0ltxlt1) from first principles.

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  6. Differentiate cos^(-1)(2x+3) from first principles.

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  7. Differentiate the following functions with respect to x : (2^2cotx)/(...

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  8. If f(x)=|cosx-sinx|,find f^(prime)(pi/6) and f^(prime)(pi/3)dot

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  9. If y=(1+x)(1+x^2)(1+x^4)(1+x^8)...........(1+x^(2n)),find dy//dx at x...

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  10. If x=asec^3theta and y=atan^3theta, find (dy)/(dx) at theta=pi/3

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  11. If x=sin^(-1)((2t)/(1+t^2))a n d \ y=tan^(-1)((2t)/(1-t^2)),t > 1. P r...

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  12. If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))),prove that (dy)/(dx)=(cosx...

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  13. If y=a^(x^(a^(x^......)^oo))), \ p rov et h a t \ (dy)/(dx)=(y^2logy...

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  14. If y=e^(x+e^(x+e^((((( tooo))))))),show that(dy)/(dx)=y/(1-y)

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  15. If y=(sqrt(x))^sqrt(x)^sqrt(x)^(dot)^(((oo))),s howt h a t(dy)/(dx)=(y...

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  16. If y=x+1/(x+1/(1/(x+))), p rov et h a t(dy)/(dx)=y/(2y-x)

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  17. If y=(sinx)/(1+(cosx)/(1+(sinx)/(1+(cosx)/(1+ tooo)))),p rov et h a t(...

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  18. If e^x+e^y=e^(x+y), prove that (dy)/(dx)=-(e^x(e^y-1))/(e^y(e^x-1))

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  19. If y=(cosx)^((((cosx)^(((cosx)^((...oo)) prove that (dy)/(dx)=-(y^2tan...

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  20. If y=sqrt(sinx+y) ,write (dy)/(dx)dot

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