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Math Help - Find derivative and simplify

  1. #1
    Junior Member
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    Find derivative and simplify

    y=csc(x^2)
    Ok on this one I know you use the chain rule? The formula for csc is -cscu cotu du/dx so should it go somthing like
    ------>y'= -csc(x^2) cot(x^2) (2x) ???

    also on
    f(x)=tan^3x
    can I rewrite it to
    -----> f(x)= (tan x)^3
    f '(x)= 3(sec^2 x)^2 (1)

    Any help would be great.
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  2. #2
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    Quote Originally Posted by Nightasylum View Post
    y=csc(x^2)
    Ok on this one I know you use the chain rule? The formula for csc is -cscu cotu du/dx so should it go somthing like
    ------>y'= -csc(x^2) cot(x^2) (2x) ???

    also on
    f(x)=tan^3x
    can I rewrite it to
    -----> f(x)= (tan x)^3
    f '(x)= 3(sec^2 x)^2 (1)

    Any help would be great.
    First one is right.

    If f(x)=(\tan(x))^3 then f'=3(\tan(x))^2*\sec^2(x). Make sense?
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  3. #3
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    f(x)=tan^3x
    can I rewrite it to
    -----> f(x)= (tan x)^3
    It is fair play for me to rewrite like that right?
    Im still a little lost on the 2nd one.
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  4. #4
    MHF Contributor
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    Quote Originally Posted by Nightasylum View Post
    f(x)=tan^3x
    can I rewrite it to
    -----> f(x)= (tan x)^3
    It is fair play for me to rewrite like that right?
    Im still a little lost on the 2nd one.
    Yes you can write it like that. The tan^3(x) notation is just used for convenience and less parentheses, but both expressions are the same.

    What if you had to take the derivative of u^3 and u is a function of x. The derivative would be 3x^2*du/dx. This is exactly what I did. The first step is the power rule then the second part is the chain rule.
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