Calculus

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Find the derivatives of the following

18. y=〖cos〗^4 x^4

ANSWER: tanx2

19. y= sinx/(1+ 〖cos〗^2 x)

ANSWER: 3sinx
20. y=sinx(sinx+cosx)

ANSWER: sinx

Can you check my answers?

  • Calculus -

    wow - remember the chain rule

    if u = cos(x^4) then we have
    y = u^4
    y' = 4u^3 u'
    y' = 4 cos^3(x^4) * (-sin(x^4)(4x^3)
    = -16x^3 sin(x^4) cos^3(x^4)

    y = sinx/(1+cos^2(x))
    y' = [(cosx)(1+cos^2(x)) - (sinx)(2cosx)(-sinx)]/(1+cos^2(x))^2

    y = sinx(sinx+cosx)
    y' = cosx(sinx+cosx) + sinx(cosx-sinx)

    I think you have some serious reviewing to do. I'd love to see the step-by-step work you did to get your answers.

  • Calculus -

    -4 cos^3 x^4 sin x^4 (4 x^3)

    = - 16 x^3 cos^3 x^4 sin x^4
    how that is tan x2 whatever that is I can not imagine

  • Calculus -

    ohhh.. I think I know what I did wrong.. I did not even realize that I was doing something completely different

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