Find dy/dx if

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Many thanks!

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- Dec 19th 2008, 03:20 AMbluebiroHelp with a differentiating question.
Find dy/dx if

(attachment)

Many thanks! - Dec 19th 2008, 04:37 AMGrandadDifferentiating
Hi-

Just differentiate $\displaystyle 2y^3t+t^3y=1$ with respect to $\displaystyle x$, using the product rule to get:

$\displaystyle 2y^3\frac{dt}{dx}+3y^2\frac{dy}{dx}t +t^3\frac{dy}{dx}+3t^2\frac{dt}{dx}y=0$

Now collect together the terms in $\displaystyle \frac{dt}{dx}$ and $\displaystyle \frac{dy}{dx}$, substitute $\displaystyle \frac{dt}{dx}=\frac{1}{\cos t}$ and the job's done.

Grandad