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Math Help - Calculus Defrentiation

  1. #1
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    Calculus Defrentiation

    Can anyone show me how to defrentiate these 4 functions please

    (3x^2-4x)^3

    (x^2+2)(2x^3-5x^2+4x)

    sqrt X - 3rd square root x not 3(sqrt x) but the 3 is very small and close to the square root sign

    and 3x/x^2+4






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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by notoriousmc View Post
    Can anyone show me how to differentiate these 4 functions please

    (3x^2-4x)^3
    hopefully you know the power rule for derivatives.

    are you aware of the chain rule?

    it says \frac d{dx}f(g(x)) = f'(g(x)) \cdot g'(x)

    here, your f(x) = x^3 and your g(x) = 3x^2 - 4x

    an example:

    y = (x^2 + 2x)^5

    \Rightarrow y' = 5(x^2 + 2x)^4 \cdot (2x + 2) = 10(x + 1)(x^2 + 2x)^4

    (x^2+2)(2x^3-5x^2+4x)
    here, apply the product rule

    it says (if f and g are functions of x), then

    \frac d{dx}[fg] = f'g + fg'

    here, your f(x) = x^2 + 2 and your g(x) = 2x^3 - 5x^2 + 4x



    sqrt X - 3rd square root x not 3(sqrt x) but the 3 is very small and close to the square root sign
    note that you can write the radicals as powers to obtain the following

    x^{1/2} - x^{1/3}

    now apply the power rule to find the derivative

    and 3x/x^2+4
    two main options here.

    (1) write as 3x(x^2 + 4)^{-1} and use the product rule with f(x) = 3x and g(x) = (x^2 + 4)^{-1}. note that you need the chain rule to find g'(x)

    (2) use the quotient rule: \frac d{dx} \left[ \frac fg \right] = \frac {f'g - fg'}{g^2}

    your f and g are the same as above
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  3. #3
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    Jhevon was faster than me.


    Quote Originally Posted by notoriousmc View Post

    (3x^2-4x)^3

    (3x^2-4x)^3= (3x^2-4x) (3x^2-4x) (3x^2-4x)
    multiply it out and take the derivative

    Quote Originally Posted by notoriousmc View Post
    (x^2+2)(2x^3-5x^2+4x)
    (x^2+2)(2x^3-5x^2+4x)
    multiply it out and take the derivative

    Quote Originally Posted by notoriousmc View Post
    Do you mean 3x/(x^2+4)?
    use quotient rule
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