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Evaluate the derivitive dy/dx at the (0,0) for the equation (2x)-(5x^3y^2)+4y=0
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High School Teacher
You simply differentiate whole expression, but when you differentiate `y` you need to remember that `y` is a function of `x` and thus `(f(y))'=f'(y)y'` in other words when you have some function of `y` you differentiate it as if it's a composition i.e. you use chain rule.
Let's now differentiate our equation.
Now leave everything with `y'` on left side and everything else on the right side.
Now to calculate the value of the derivative at (0,0) we simply put zeros instead of x and y.
`dy/dx(0,0)=(15cdot0cdot0-2)/(4-10cdot0cdot0)=-2/4=-1/2` <-- Your solution
In the attached image blue is the curve defined by your equation and red is the tangent line at point (0,0).
Posted by tiburtius on October 31, 2013 at 5:21 PM (Answer #1)
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