Question

7. Find the derivative of 2x³+ 3y² = 7xy

Answer 1

Step 1: Write out the expression

`2x^3+3y^2=7xy`

Step 2: Differentiate implicitly

`\begin{gathered} 6x^2+6yy^(\prime)=7(xy^(\prime)+y) \\ \text{ Wh}ere \\ y^(\prime)=\frac{\text{ dy}}{dx} \end{gathered}`

Step 4: Isolate y'

`\begin{gathered} 6x^2+6yy^(\prime)=7xy^(\prime)+7y \\ 6yy^(\prime)-7xy^(\prime)=7y-6x^2 \\ y^(\prime)(6y-7x)=7y-6x^2 \\ \text{Dividing both sides by }6y-7x,\text{ we have} \end{gathered}`
`y^(\prime)=(7y-6x^2)/(6y-7x)`

Hence the derivative is

`(7y-6x^2)/(6y-7x)`

(7y - 6x²)/(6y - 7x)