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Find the derivative of the following fun...

Find the derivative of the following functions:
(i) `sin x cos x` (ii) `sec x`
(iii) `5sec x+4 cos x` (iv) `cosec x`
(v) `3 cot x+5 cosec x` (vi) `5sinx-6cosx+7`
(vii) `2tanx-7secx`

Text Solution

AI Generated Solution

To find the derivatives of the given functions, we will apply the rules of differentiation step by step. ### (i) Derivative of `sin x cos x` Using the product rule, which states that if \( u = \sin x \) and \( v = \cos x \), then: \[ \frac{d}{dx}(uv) = u'v + uv' ...
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Knowledge Check

  • If cosec x + cot x = a , then cos x is

    A
    `(a-1)/( a^2 + 1)`
    B
    `(a^2 - 1)/( a^2 + 1)`
    C
    `(2a)/( a^2 + 1)`
    D
    `(2a)/( a^2 -1)`

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