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if e^x+e^y=e^(x+y) then show that (dy)/(...

if `e^x+e^y=e^(x+y)` then show that `(dy)/(dx)+e^(y-x)=0`.

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SHARAM PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXAMPLE
  1. Write the derivative of sinx with respect to cosx.

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  2. If y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^(2))] then find (dy)/(dx)

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  3. if e^x+e^y=e^(x+y) then show that (dy)/(dx)+e^(y-x)=0.

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  4. Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) w.r.t. sin^(-1)(2xsqrt(1-x...

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  5. Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) w.r.t. sin^(-1)(2xsqrt(1-x...

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  6. Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) w.r.t sin^(-1)((2x)/(1+x^2))...

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  7. Write that condition of Rolle’s theorem which is violated by the funct...

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  8. If f(0)=0,f'(0)=2 then what is the derivative of y = f(f(f(f(x)))) at...

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  9. If y = tan^(-1)(1/(1+x+x^2)) + tan^(-1)(1/(x^2+3x+3)) + tan^(-1)(1/(x^...

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  10. If x=a(cos t + log tan (t/2)),y=a sin t, then what is (d^2y)/(dx^2) at...

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  11. What is the first derivative of cos^(-1) (sin(sqrt(1+x)/2))+x^x w.r.t ...

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  12. If f(x)=|logx| then for x!=1, then what is f'(x)?

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  13. If y=|cosx|+|sinx| then what is (dy)/(dx) at x = (2pi)/3 ?

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  14. If f(x)=logx^(2)(logx), then f(e)

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  15. If y = tan^(-1)[(x/log ex^3)] + tan^(-1)[(5 + 3logx)/(1-15logx)] then ...

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  16. If f(x) = a |sinx| + b.e^(|x|) + c |x|^3 and f(x) is differentiable at...

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  17. What is the value ofthe derivative of f(x)=|x-1|+|x-3| at x=2?

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  18. If f(x+y) = f(x) f(y) for all x,y and if f(5) = 2 and f(0) = 3, then w...

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  19. Write the derivative of e^(3 logx) "w.r.t.x"^(2)

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  20. Differentiate a^(lnx) w.r.t x ^(2).

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