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If y=(1+1/x)^x , then (dy)/(dx)= (a)(1+...

If `y=(1+1/x)^x` , then `(dy)/(dx)=` (a)`(1+1/x)^x{log(1+1/x)-1/(x+1)}` (b) `(1+1/x)^xlog(1+1/x)` (c) `(x+1/x)^x{log(x+1)-x/(x+1)}` (d) `(x+1/x)^x{log(1+1/x)+1/(x+1)}`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differential coefficient of sec(tan^(-1)x) is (a)x/(1+x^2) (b) xsqrt...

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

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  3. If y=(1+1/x)^x , then (dy)/(dx)= (a)(1+1/x)^x{log(1+1/x)-1/(x+1)} (b)...

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  4. If x^y=e^(x-y) , then (dy)/(dx) is (a)(1+x)/(1+logx) (b) (1-logx)/(1+l...

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  5. Given f(x)=4x^8 , then (a)f'(1/2)=f'(-1/2) (b) f(1/2)=-f'(-1/2) (c) f...

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  6. If x=a\ cos^3theta,\ \ y=a\ sin^3theta , then sqrt(1+((dy)/(dx))^2)= ...

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  7. If y=sin^(-1)((1-x^2)/(1+x^2)) , then (dy)/(dx)= (a)-2/(1+x^2) (b) 2/...

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  8. The derivative of sec^(-1)(1/(2x^2-1)) with respect to sqrt(1+3x) at x...

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  9. For the curve sqrt(x)+sqrt(y)=1 , (dy)/(dx) at (1//4,\ 1//4) is (a)...

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  10. If sin(x+y)=log(x+y) , then (dy)/(dx)= (a) 2 (b) -2 (c) 1 (d)...

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  11. Let U=sin^(-1)((2x)/(1+x^2)) and V=tan^(-1)((2x)/(1-x^2)) , then (d U)...

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  12. d/ dx { tan^ −1 ( cosx/ (1+sinx) ) } equals (a)1...

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  13. d/(dx)[log{e^x((x-2)/(x+2))^(3//4)}] equals (a) (x^2-1)/(x^2-4) (b...

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  14. If y=sqrt(sinx+y) , then (dy)/(dx)= (a)(sinx)/(2y-1) (b) (sinx)/(...

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  15. If 3sin(x y)+4cos(x y)=5 , then (dy)/(dx)= (a) y/x (b) (3sin(x y)+4...

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  16. If siny=xsin(a+y) , then (dy)/(dx) is (a)(sina)/(sina sin^2(a+y)) (...

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  17. The derivative of cos^(-1)(2x^2-1) with respect to cos^(-1)x is (a) ...

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  18. If f(x)=sqrt(x^2+6x+9) , then f^(prime)(x) is equal to (a) 1 for x<-3 ...

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  19. If f(x)=|x^2-9x+20| , then f^(prime)(x) is equal to (a) -2x+9 for all ...

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  20. If f(x)=sqrt(x^2-10 x+25) , then the derivative of f(x) in the inte...

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