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Differentiate log{x+2+sqrt(x^2+4x+1)} wi...

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

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To differentiate the function \( y = \log(x + 2 + \sqrt{x^2 + 4x + 1}) \) with respect to \( x \), we will apply the chain rule and the properties of logarithmic differentiation. ### Step-by-Step Solution: 1. **Identify the function**: \[ y = \log(x + 2 + \sqrt{x^2 + 4x + 1}) \] ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate e^x \ logsin2x with respect to x .

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

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

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

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

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

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

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

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

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

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  11. Differentiate the following functions with respect to e^(a x)secxta...

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  12. Differentiate log(cosx^2) with respect to x :

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  13. Differentiate cos(logx)^2 with respect to x :

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  14. Differentiate logsqrt((x-1)/(x+1)) with respect to x :

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  15. If y=log{sqrt(x-1)-sqrt(x+1)} , show that (dy)/(dx)=(-1)/(2sqrt(x^2-1)...

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  16. If y=sqrt(x+1)+sqrt(x-1) , prove that sqrt(x^2-1)(dy)/(dx)=1/2y

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  17. If y=x/(x+2) , prove that x(dy)/(dx)=(1-y)y

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  18. If y=log(sqrt(x)+1/(sqrt(x))) , prove that (dy)/(dx)=(x-1)/(2x(x+1))

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  19. If y=logsqrt((1-tanx)/(1+tanx)) , prove that (dy)/(dx)=-sec2x .

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  20. If y=sqrt(x)+1/(sqrt(x)) , prove that 2x(dy)/(dx)=sqrt(x)-1/(sqrt(x))

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