Calculus

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Can someone help me find the derivatives of these questions?

For these can you only need to tell me the answer so i can see if i have the same thing.
y=cos(-4x)

y = sinx^2

y = xcosx


I need help with these 6 please.

y = xcos(1/x)

y = (1+sinx)/(1-sin^(2)x)

y = sin^2x/cosx

y = sqrt(sin(sqrtx))

y = 3sqrt(xcosx)

y = 1/(sin(x-sinx)

  • Calculus -

    y=cos(-4x)
    y' = -4(-sin(-4x)
    = 4sin(-4x)

    y = sinx^2 or (sinx)^2

    y' = 2sinxcosx or sin 2x


    y = xcosx
    y' = x(-sinx) + (1)cosx
    = cosx - xsinx

  • Calculus -

    for y = xcos(1/x)
    I would use the product rule

    y' = x(-sin(1/x))(-1/x^2) + (1)cos(1/x)



    for y = (1+sinx)/(1-sin^(2)x) I would reduce it to

    y = (1+sinx)/((1+sinx)(1-sinx))
    = 1/(1-sinx)
    = (1-sinx)^-1

    now y' = -1(1-sinx)-2?sup>(-cosx)

    why don't you show me some of the steps you have sofar for the others?

  • Calculus -

    last line should have come out as ...

    y = -1(1-sinx)-2(-cosx)

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