## Orthogonal Trajectory Problem

I am working on this problem, and have a simple question.

Determine the orthogonal trajectory of
$$x^p + Cy^p = 1$$
where p = constant.

I start out by taking the derivative with respect to x. My question is this. does
$$Cy^p$$ become $$Cpy^{p-1}$$ or $$C_1y^{p-1}$$ ?

Thanks,
Morgan
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 Recognitions: Gold Member Science Advisor Staff Emeritus C1?? There isn't any "C1" in your original formula! The derivative of yp with respect to y is pyp-1. The derivative of Cyp with respect to y is Cpyp-1. By the chail law, the derivative of Cyp is $Cpy^{p-1}\frac{dy}{dx}$. Solve the resulting equation for $\frac{dy}{dx}$ to find the slope of the tangent line to the original trajectory at each point.
 If p is a constant and C is a constant isn't $$C_1$$ just another constant? Isn't $$C_1y^{p-1}\frac{dy} {dx}$$ the same as what you have? Thanks for pointing out the chain rule, I missed that.