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Math Help - derivative question

  1. #1
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    derivative question

    im doing question

    f(x) = (x^2 - [e^(2x)] + [sin^3 (x)])^7, find f'(x)

    so far,
    f'(x)= 7(x^2 - [e^(2x)] + [sin^3 (x)])^6 * (x^2 - [e^(2x)] + [sin^3 (x)])'
    = 7(x^2 - [e^(2x)] + [sin^3 (x)])^6 *@@@@@@@@@@@@@@

    for @@@@@@@@...
    i know i have to derivate (x^2 - [e^(2x)] + [sin^3 (x)])'
    i was wondering if i just derivate like 2x - 2e^2x + 3(sinx)^2 (cosx) ?

    if so, do i have to derivate "x" from"
    (sinx)^3
    3(sinx)^2 (cosx) <--- from here, do i have to derivate "x"? like 3(sinx)^2 (cosx)(x)' ?
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  2. #2
    Member mathemagister's Avatar
    Joined
    Feb 2010
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    Quote Originally Posted by haebinpark View Post
    im doing question

    f(x) = (x^2 - [e^(2x)] + [sin^3 (x)])^7, find f'(x)

    so far,
    f'(x)= 7(x^2 - [e^(2x)] + [sin^3 (x)])^6 * (x^2 - [e^(2x)] + [sin^3 (x)])'
    = 7(x^2 - [e^(2x)] + [sin^3 (x)])^6 *@@@@@@@@@@@@@@

    for @@@@@@@@...
    i know i have to derivate (x^2 - [e^(2x)] + [sin^3 (x)])'
    i was wondering if i just derivate like 2x - 2e^2x + 3(sinx)^2 (cosx) ?

    if so, do i have to derivate "x" from"
    (sinx)^3
    3(sinx)^2 (cosx) <--- from here, do i have to derivate "x"? like 3(sinx)^2 (cosx)(x)' ?
    I explained to you about the derivative of the 'x' in the other thread. You understand it, right?

    f(x) = (x^2 - e^{2x} + sin^3x)^7
    f'(x) = 7(x^2 - e^{2x} + sin^3x)^6 \times (2x - e^{2x} \times 2 + 3sin^2x \times cosx)

    I've pointed out the places where I've multiplied something because of the chain rule with \times. Do you see how that works. If you need anymore help, feel free to ask.

    Hope I helped you
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