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Differentiate the following functions wi...

Differentiate the following functions with respect to `x :` `(2^2cotx)/(sqrt(x))` (ii) `e^xlogsqrt(x)tanx`

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Let's solve the differentiation of the given functions step by step. ### Part (i): Differentiate \( y = \frac{4 \cot x}{\sqrt{x}} \) 1. **Identify the function**: \[ y = \frac{4 \cot x}{\sqrt{x}} \] ...
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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate sin^(-1)sqrt(x)(0ltxlt1) from first principles.

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

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

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

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

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

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

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

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

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

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

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

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

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  17. If y=x^x^x^ddot^((((oo)))), (dy)/(dx) is

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  18. If y=x^(tanx)+sqrt((x^2+1)/2),fin d(dy)/(dx)

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  19. If x^y=y^x ,then find (dy)/(dx)

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  20. If (sin"x")^y=(cos"y")^x, prove that (dy)/(dx)=(logcosy-ycotx)/(logsin...

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