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Differentiate sin(2\ sin^(-1)x) with res...

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

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AI Generated Solution

To differentiate the function \( y = \sin(2 \sin^{-1} x) \) with respect to \( x \), we will use the chain rule. Here’s a step-by-step solution: ### Step 1: Identify the outer and inner functions We can express \( y \) as: \[ y = \sin(u) \] where \( u = 2 \sin^{-1} x \). ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate tan^(-1)(e^x) with respect to x :

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Differentiate (x^2(1-x^2)^3)/(cos2x) with respect to x .

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  20. Differentiate log{cot(pi/4+x/2)} with respect to x :

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