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Find the derivative of(i) (x^5-cosx)/(si...

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

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To find the derivatives of the given functions using the quotient rule, we will follow these steps: ### Part (i): Derivative of \((x^5 - \cos x) / \sin x\) 1. **Identify \(u\) and \(v\)**: - Let \(u = x^5 - \cos x\) - Let \(v = \sin x\) ...
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Knowledge Check

  • The derivative of ln(x+sinx) with respect to (x+cosx) is

    A
    `(1+cosx)/((x+sinx)(1-sinx))`
    B
    `(1-cosx)/((x+sinx)(1+sinx))`
    C
    `(1-cosx)/((x-sinx)(1+cosx))`
    D
    `(1+cosx)/((x-sinx)(1-cosx))`

  • The derivative of ln(x+sinx) with respect to (x+cosx) is

    A
    `(1+cosx)/((x+sinx)(1-sinx))`
    B
    `(1-cosx)/((x+sinx)(1+sinx))`
    C
    `(1-cosx)/((x-sinx)(1+cosx))`
    D
    `(1+cosx)/((x-sinx)(1-cosx))`

  • Find the derivative of tan^(-1)((cosx+sinx)/(cosx-sinx)) with respect to x.

    A
    0
    B
    1
    C
    `-1`
    D
    `cos^2 x`

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    ((sinx - x cosx)/(x sinx + cos x ))

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