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Math Help - Derviative

  1. #1
    Senior Member polymerase's Avatar
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    Derviative

    If f is a function such that 2f(x)+x(f(x))^3=x^2, find the value of f'(2)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by polymerase View Post
    If f is a function such that 2f(x)+x(f(x))^3=x^2, find the value of f'(2)
    By the chain rule(and product rule):

    2 f(x) + x(f(x))^3 = x^2 \implies 2 f'(x) + (f(x))^3 + 3x(f(x))^2 \cdot f'(x) = 2x

    now solve for f'(x) and you can find f'(2)

    note, you will need the value for f(2), but no worries, you can find that from the original equation given.
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