Question

Please I need help with this

Determine dy/dx if
`y^3-x^2=y^2-5x`

Answer 1

`\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 ❞