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Differentiate (2^xcotx)/(sqrt(x)) with r...

Differentiate `(2^xcotx)/(sqrt(x))` with respect to `x` .

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To differentiate the function \(\frac{2^x \cot x}{\sqrt{x}}\) with respect to \(x\), we will use the quotient rule and the product rule. Let's go through the steps systematically. ### Step-by-Step Solution: 1. **Identify the function**: \[ y = \frac{2^x \cot x}{\sqrt{x}} \] ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate the following functions with respect to x : tan^(-1){sqr...

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  2. Differentiate the following functions with respect to x : tan^(-1)(s...

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  3. Differentiate (2^xcotx)/(sqrt(x)) with respect to x .

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  4. Differentiate e^xlogsqrt(x)tanx with respect to x .

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  5. Differentiate (e^x+sinx)/(1+logx) with respect to x .

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  6. Differentiate (sinx-xcosx)/(xsinx+cosx) with respect to xdot

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  7. If y=(1+x)(1+x^2)(1+x^4)(1+x^8)dot(1+x^2^n) , find (dy)/(dx) .

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  8. If f(x)=|cosx| , find f^(prime)(pi/4) and f^(prime)((3pi)/4) .

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  9. If f(x)=|cosx-sinx| , find f^(prime)(pi/6) and f^(prime)(pi/3) .

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  10. If f(x)=|logx| , x >0 , find f^(prime)(1//e) and f^(prime)(e) .

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  11. Differentiate e^(x^2) with respect to x from first-principles

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  12. Differentiate e^(2x) with respect to x from first principles

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  13. Differentiate e^(sqrt(x)) with respect to x from first-principles

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  14. Differentiate e^(sinx) with respect to x from first-principles

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  15. Differentiate x e^x from first principles.

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  16. Differentiate logsinx by first principles.

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  17. Differentiate logsecx from first principles.

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  18. If f(x)=xtan^(-1)x , find f^(prime)(1) using the first principle.

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  19. Differentiate cos^(-1)(2x+3) from first principles.

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  20. Differentiate e^(sqrt(tanx)) from first principles

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