Derviative

**polymerase** · November 6th 2007, 09:23 AM

If f is a function such that $2f(x)+x(f(x))^3=x^2$ , find the value of $f'(2)$

**Jhevon** · November 6th 2007, 09:29 AM

Originally Posted by polymerase

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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