Question

Find ds/dx on the curve

Answer 1

\[6xy=x^4+3\]

Answer 2

you mean dy/dx?

Answer 3

no it is ds/dx , the length of curve I think?

Answer 4

well its implict differentiation..not sure why ds/dx

Answer 5

@dpalnc please help? thanks! :-)

Answer 6

ds/dx would not be the length of a curve
you want arc length?

Answer 7

\[ds=\sqrt{(\frac{dy}{dx})^2+1}\]

Answer 8

get that and take the derivative with respect to x I guess

Answer 9

\[6xy=x^4+3\]
taking the derivative of both sides with respect to x
\[6y+6x\frac{\text dy}{\text dx}=4x^3\]

Answer 10

oh you don't need to take the derivative, just rearrange it a bit (I mistyped the arc length differential before)\[ds=\sqrt{(\frac{dy}{dx})^2+1}dx\implies\frac{ds}{dx}=\sqrt{(\frac{dy}{dx})^2+1}\]use the method Unkle outlines above