Please I need help with this Determine dy/dx if y^3-x^2=y^2-5x

Question

asked Aug 23, 2023 139k views

1 Answer

Stenerson · Answer 1 · 2023-08-28T12:52:05+0000

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \:(dy)/(dx) = (2x - 5)/(3y² - 2y)$

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$\large \tt Solution \: :$

$\qquad \tt \rightarrow \: {y}^(3) - {x}^(2) = {y}^(2) - 5x$

[ take derivative with respect to x, on both sides of the equality ]

$\qquad \tt \rightarrow \: (d)/(dx) ( {y}^(3) - {x}^(2) ) = (d)/(dx) ( {y}^(2) - 5x)$

$\qquad \tt \rightarrow \: (d)/(dx) ( {y}^(3)) - (d)/(dx) ({x}^(2) ) = (d)/(dx) ( {y}^(2)) - (d)/(dx) (5x)$

$\qquad \tt \rightarrow \: 3 {y}^(2) \sdot (dy)/(dx) - 2x = 2y \sdot (dy)/(dx) - 5$

[ By chain rule ]

$\qquad \tt \rightarrow \: 3 {y}^(2) \sdot (dy)/(dx) - 2y \sdot (dy)/(dx) = 2x - 5$

[ take dy/dx common out ]

$\qquad \tt \rightarrow \: (dy)/(dx) (3 {y}^(2) - 2y)= 2x - 5$

$\qquad \tt \rightarrow \: (dy)/(dx) = \frac{ 2x - 5}{3 {y}^(2) - 2y}$

I hope you understood the whole procedure, let me know if you have any problem regarding the steps !

Answered by : ❝ AǫᴜᴀWɪᴢ ❞