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Differentiate sqrt(sin3x) from the first...

Differentiate `sqrt(sin3x)` from the first principle.

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To differentiate \( y = \sqrt{\sin(3x)} \) using the first principle of differentiation, we will follow the steps outlined below: ### Step 1: Define the function and the increment Let \( y = \sqrt{\sin(3x)} \). We will consider a small increment \( \Delta x \) in \( x \), which leads to a corresponding increment \( \Delta y \) in \( y \). ### Step 2: Express \( \Delta y \) The increment \( \Delta y \) can be expressed as: \[ ...
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RS AGGARWAL-DIFFERENTIATION-Solved Examples
  1. Find the derivative of x^(-3//2) from the first principle .

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  2. Find the derivative of (1)/(x^(2)) from the first principle .

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  3. Differentiate sqrt(sin3x) from the first principle.

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  4. Find the derivative of e^(sqrt(x)) from the first principle.

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  5. Find the derivative of e^(x^(2)) from the first principle.

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  6. Find the derivative of e^(sinx ) from the first principle.

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  7. Differentiate each of the following from the first principle. (i) sq...

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  8. Differentiate each of the following from the first principle . (i) s...

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  9. Find the derivative of the following from the first principle . (i) ...

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  10. Find the derivative of the following from the first principle. (i) s...

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  11. Differentiate x e^x from first principles.

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  12. Differentiate the following functions w.r.t.x from the first principle...

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  13. Differentiate :(i) xe^(x) , (ii) x^(2)e^(x) sin x

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  14. Differentiate :(i) xe^(x) , (ii) x^(2)e^(x) sin x

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  15. Differentiate : x^(2) tan x

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  16. Differentiate (e^(x) sin x + x^(p) cos x)

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  17. Differentiate e^(x)(x^(3) +sqrtx)

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  18. Differentatiate ((e^(x)cos x)/x^(3)) using the product rule .

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  19. Differentiate : (i) (e^(x))/(x) , (ii) ((2x+3)/(x^(2) - 5)) , (iii) ...

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  20. Differentiate ((x^(2) + 5x -6)/(4x^(2) -x+3))

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