Find the derivative of the following functions from first princi

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 Multiple Choice QuestionsShort Answer Type

21.

Evaluate space space limit as straight x rightwards arrow straight x over 4 of fraction numerator cos space straight x space minus space sin space straight x over denominator straight x minus straight pi divided by 4 end fraction.

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22.

Evaluate space space space space space limit as straight x rightwards arrow straight pi of fraction numerator sin left parenthesis straight n minus straight pi right parenthesis over denominator straight pi left parenthesis straight pi minus straight x right parenthesis end fraction.

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23.

Evaluate space space space space space space space space space space space space limit as straight x rightwards arrow 0 of fraction numerator sin space space ax plus bx over denominator ax plus sin space bx end fraction comma space straight a comma space space straight b comma space straight a plus straight b not equal to 0

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24.

Evaluate space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space limit as straight x rightwards arrow 0 of left parenthesis cosec space straight x minus cot space straight x right parenthesis

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25. Find the derivative of x2-2 at x = 10.
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26. Find the derivative of f (x) = 7 at x = 3
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27.

Find the derivative of space fraction numerator 1 over denominator square root of 3 straight x plus 1 end root end fraction at x =2.

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28. Find the derivative of the following functions from first principle. 

(x-1) (x-2)


Let   f(x) = (x-1)(x-2) = x-3x + 2.

∴      space space space space space space space space space space space space space space straight f space left parenthesis straight x right parenthesis space equals space limit as straight h rightwards arrow 0 of fraction numerator straight f left parenthesis straight x plus straight h right parenthesis minus straight f left parenthesis straight x right parenthesis over denominator straight h end fraction

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#6 {main}</pre>

     space space space space space space space space space space space space space space space space space space equals space limit as straight h rightwards arrow 0 of fraction numerator straight x squared plus 2 hx plus straight h squared minus negative 3 straight x minus 3 straight h plus 2 minus straight x squared plus 3 straight x minus 2 over denominator straight h end fraction

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#6 {main}</pre>

                    = 0 + 2x-3 = 2x -3


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29. Find the derivative of the following functions from first principle. 

space space space space space fraction numerator straight x plus 1 over denominator straight x minus 1 end fraction
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30.

Find the derivative of f(x) = 

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