# Calculus

posted by StevE

Find the derivatives of the following

18. y=〖cos〗^4 x^4

19. y= sinx/(1+ 〖cos〗^2 x)

20. y=sinx(sinx+cosx)

Can you check my answers?

1. Steve

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.

2. Damon

-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

3. StevE

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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