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Find the derivative of f (x) from the fi...

Find the derivative of f (x) from the first principles, where f(x) is (i) `sin x + cos x`

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To find the derivative of the function \( f(x) = \sin x + \cos x \) from first principles, we will use the definition of the derivative: \[ f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} \] ### Step-by-Step Solution: ...
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Knowledge Check

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

    A
    `(-2)/(x)`
    B
    `2/(x^(3))`
    C
    `(-2)/(x^(2))`
    D
    `(-2)/(x^(3))`
  • NCERT-LIMITS AND DERIVATIVES-SOLVED EXAMPLES
    1. Find the derivative of f (x) from the first principles, where f(x) is...

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    2. Find the derivative of(i) (x^5-cosx)/(sinx) (ii) (x+cosx)/(tanx)

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    3. Compute derivative of (i) f (x) = sin 2x (ii) g(x) = cot x

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    4. Find the derivative of f(x)=x^2

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    5. Find the derivative of the constant function f(x) = afor a fixed real...

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    6. Find the derivative of f(x) =1/x

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    7. Compute the derivative of 6x^(100)-x^(55)+x.

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    8. Find the derivative of f(x) =1+x+x^2+x^3+.......+x^(50)at x = 1.

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    9. Find the derivative of f(x) =(x+1)/x.

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    10. Compute the derivative of sin x by first principle.

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    11. Compute the derivative of tan x.

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    12. Compute the derivative of f(x)=sin^2x.

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    13. Find the derivative of f from the first principles, where f is given ...

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    14. Evaluate(i) (lim)(x->1)(x^(15)-1)/(x^(10)-1) (ii) (lim)(x->0)(sqrt(1+x...

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    15. Find the limits (i) lim(x->1)[(x^2+1)/(x+100)] (ii) lim(x->2)[(x^3-4x^...

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    16. Find the limits: (i) lim(x->1)[x^3-x^2+1] (iii) lim(x->3)[x(x+1)](iii)...

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    17. Find the derivative of sin x at x = 0.

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    18. Find the derivative of the function f(x)=2x^2+3x-5at x = -1. Also pro...

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    19. Find the derivative at x = 2of the function f(x) = 3x.

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    20. Evaluate (i) lim(x->0)(sin4x)/(sin2x) (ii) lim(x->0)(tanx)/x

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