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If y=x^x , find (dy)/(dx) at x=e ....

If `y=x^x` , find `(dy)/(dx)` at `x=e` .

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y=sin^(-1)x+cos^(-1)x ,\ find (dy)/(dx) .

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  2. If x=a(theta+sintheta),\ \ y=a(1+costheta) , find (dy)/(dx) .

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  3. If y=x^x , find (dy)/(dx) at x=e .

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  4. If y=tan^(-1)((1-x)/(1+x)) , find (dy)/(dx) .

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  5. If y=(log)a x , find (dy)/(dx) .

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  6. If y=logsqrt(tanx) , write (dy)/(dx) .

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  7. If y=sin^(-1)((1-x^2)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) , find (dy)/(...

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  8. If y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0. Find (dy)/(dx)...

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  9. If |x|<1 and y=1+x+x^2+\ ddotto\ oo , then find the value of (dy)/(...

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  10. If u=sin^(-1)((2x)/(1+x^2)) and v=tan^(-1)((2x)/(1-x^2)) , where -1<x<...

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  11. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

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  12. If y=log(3x),\ \ x!=0 , find (dy)/(dx) .

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  13. If f(x) is an even function, then write whether f^(prime)(x) is eve...

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  14. If f(x) is an odd function, then write whether f^(prime)(x) is even...

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  15. Write the derivative of sinx w.r.t. cosxdot

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  16. If f(x)=(log)(x^2)(logx) , then f^(prime)(x) at x=e is (a) 0 (b) 1 (c)...

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  17. The differential coefficient of f(logx) with respect to x , where f(...

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  18. The derivative of the function cot^(-1){(cos2x)^(1//2)} at x=pi//6 i...

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  19. Differential coefficient of sec(tan^(-1)x) is (a)x/(1+x^2) (b) xsqrt...

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  20. If y= tan^(-1)sqrt((1-sinx)/(1+sinx)), then the value of (dy)/(dx) at ...

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