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Differentiate tan^(-1)(e^x) with respect...

Differentiate `tan^(-1)(e^x)` with respect to `x` :

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To differentiate \( y = \tan^{-1}(e^x) \) with respect to \( x \), we will use the chain rule and the derivative of the inverse tangent function. ### Step-by-step Solution: 1. **Identify the function**: Let \( y = \tan^{-1}(u) \) where \( u = e^x \). 2. **Differentiate using the chain rule**: ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate (e^(2x)+e^(-2x))/(e^(2x)-e^(-2x)) with respect to x .

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  2. Differentiate log((x^2+x+1)/(x^2-x+1)) with respect to x .

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  3. Differentiate tan^(-1)(e^x) with respect to x :

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  4. Differentiate: e^(sin^(-1) \ 2x) with respect to x .

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  5. Differentiate sin(2\ sin^(-1)x) with respect to x :

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  6. Differentiate e^(tan^(-1)sqrt(x)) with respect to x .

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  7. Differentiate sqrt(tan^(-1)(x/2)) with respect to x :

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  8. Differentiate log(tan^(-1)x) with respect to x :

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  9. Differentiate the following functions with respect to (2^xcosx)/((x...

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  10. Differentiate xsin2x+5^x+k^k+(t a n^2x)^3 with respect to x :

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  11. Differentiate log(3x+2)-x^2log(2x-1) with respect to x :

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  12. Differentiate sin^2{log(2x+3)} with respect to x :

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  13. Differentiate e^x \ logsin2x with respect to x .

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  14. Differentiate (sqrt(x^2+1)+sqrt(x^2-1))/(sqrt(x^2+1)-sqrt(x^2-1)) with...

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  15. Differentiate log{x+2+sqrt(x^2+4x+1)} with respect to x :

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  16. Differentiate (sin^(-1)x^4)^4 with respect to x :

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  17. Differentiate sin^(-1)(x/(sqrt(x^2+a^2))) with respect to x :

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  18. Differentiate (e^xsinx)/((x^2+2)^3) with respect to x .

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  19. Differentiate 3\ e^(-3x)log(1+x)

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  20. Differentiate the following functions with respect to (x^2+2)/(sqrt...

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