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Differentiate the following function ...

Differentiate the following function `3e^(-3x)"log"(1+x)`

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To differentiate the function \( y = 3e^{-3x} \log(1+x) \), we will use the product rule of differentiation. The product rule states that if we have two functions \( u \) and \( v \), then the derivative of their product is given by: \[ \frac{dy}{dx} = u'v + uv' \] ### Step 1: Identify the functions Let: ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate the following functions with respect to x : (i)log(c...

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  2. Find (dy)/(dx), y=x^x+x^(1/x)

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  3. Differentiate the following function 3e^(-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. If y=log{sqrt(x-1)-sqrt(x+1)}, show that (dy)/(dx)=(-1)/(2sqrt(x^2-1))

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  6. Find (dy)/(dx) in each of the following: 4x+3y="log"(4x-3y)

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  7. Find (dy)/(dx) in each of the following: x^(2/3)+y^(2/3)=a^(2/3)

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  8. Find (dy)/(dx) in each of the following: x y=c^2

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  9. Differentiate the following function with respect to x : cos^(-1){(x+...

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  10. Differentiate the following function with respect to x : sin^(-1){...

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  11. Differentiate the following function with respect to x : t a n^(-1...

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  12. Differentiate the following function with respect to x : sin^(-1...

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  13. Differentiate the following function with respect to x : tan^-1(x/(...

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  14. Differentiate the following functions with respect to 3^{x^2}+2x

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  15. Differentiate the following function from first principles: e^(3x)

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  16. Differentiate the following functions with respect to 3^{e^x}

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  17. Differentiate the following function with respect to x : sin ^{-1}{...

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  18. Differentiate the following functions with respect to sqrt((1-x^2)/...

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  19. Differentiate the following functions with respect to e^(tanx)

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  20. Differentiate the following function sin^(-1)(x/(x^2+a^2))

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