Question

4x^2 + 5xy − y^2 = 2 implicit differentiation

Answer 1

8x + 5xdy/dx +5y - 2y dy/dx =0

(5x-2y)dy/dx = -8x - 5y

dy/dx = ( -8x - 5y) / (5x-2y)

Answer 2

Differentiate both sides with respect to x. And then re-arrange to solve for dy/dx.\[8x+5y+5x\frac{ dy }{ dx }-2y \frac{ dy }{ dx }=0 \rightarrow 5x\frac{ dy }{ dx }-2y \frac{ dy }{ dx }=-8x-5y\]\[\rightarrow \frac{ dy }{ dx }(5x-2y) =-8x-5y \rightarrow \frac{ dy }{ dx }=-\frac{ 8x+5 }{ 5x-2y }\]

@sallyxx

Answer 3

Sorry, I forgot the y in dy/dx. Should be like this:\[\rightarrow \frac{ dy }{ dx }(5x-2y) =-8x-5y \rightarrow \frac{ dy }{ dx }=-\frac{ 8x+5y }{ 5x-2y }\]

@sallyxx

Answer 4

thank you, sorry to be annoying but then it's asking for the y' of it