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Thread: Derviative

  1. #1
    Senior Member polymerase's Avatar
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    Derviative

    If f is a function such that $\displaystyle 2f(x)+x(f(x))^3=x^2$, find the value of $\displaystyle f'(2)$
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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 $\displaystyle 2f(x)+x(f(x))^3=x^2$, find the value of $\displaystyle f'(2)$
    By the chain rule(and product rule):

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

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

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