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

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

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To differentiate the function \( y = 3 e^{-3x} \log(1+x) \), we will use the product rule and the chain rule. ### Step-by-Step Solution: 1. **Identify the components of the function**: We have two functions multiplied together: - \( u = e^{-3x} \) - \( v = \log(1+x) \) ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate sin^(-1)(x/(sqrt(x^2+a^2))) with respect to x :

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. If y=e^xcosx , prove that (dy)/(dx)=sqrt(2)\ e^xcos(x+pi/4)

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