Derivative: sec4x tan4x + 8x/(1+x^4)

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SUMMARY

The derivative of the function sec(4x) tan(4x) + 8x/(1+x^4) is calculated using the chain rule and product rule. The correct derivative is 4sec(4x)tan(4x) + 8/(1+x^4) + 8x(-4)/(1+x^4)^2. The discussion clarifies the necessity of multiplying by the derivative of the inner function, which is 4 in this case. The final expression simplifies to 4sec(4x)tan(4x) + 8/(1+x^4) - 32x^2/(1+x^4)^2.

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helpm3pl3ase
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(sec4x + 4arctanx^2)=

(sec4x)(tan4x) + (4)(1/1+x^4)(2x).. Did I derive this correctly??
 
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Did you use the chain rule on the sec(4x) term?
 
you forgot to multiply by du = 4 in the first term
 
(sec4x)(4)(tan4x)(4) + (4)(1/1+x^4)(2x)

or

16(sec4x)(tan4x) + (4)(1/1+x^4)(2x)??
 
or do i keep just 1 4?? like this..

(sec4x)(tan4x)(4) + (4)(1/1+x^4)(2x)
 
It would only be one four. Let sec(4x)=sec(u).

Then d(sec4x)/dx = d(secu)/dx = secu*tanu*du/dx

du/dx = 4, so

sec(4x)' = 4sec(4x)tan(4x)
 

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