{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Calc03_7 - 3.7 Implicit Differentiation By...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
3.7 Implicit Differentiation By leonardogillesfleur
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
y 1 = ξ ψ 2 =- ξ y 1 = 2 3 9- ξ 2 ψ 2 =- 2 3 9- ξ 2 y 1 = ξ 2 ψ 2 =- ξ 2 y 1 = 9- ξ 2 ψ 2 =- 9- ξ 2 y 1 = 2 ξ + 3- ξ 2 ψ 2 =- 2 ξ + 3- ξ 2
Background image of page 2
y = 4 x - y +2 xy x 2 y = y + x cos x sin x - x y = x y 2 x 2 - y + x
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
x 3 2 - ξ 5 6 x - 1 2 - ξ - 5 6
Background image of page 4
2 2 1 x y + = This is not a function, but it would still be nice to be able to find the slope. 2 2 1 d d d x y dx dx dx + = Do the same thing to both sides. 2 2 0 dy x y dx + = Note use of chain rule. 2 2 dy y x dx = - 2 2 dy x dx y - = dy x dx y = -
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 2 sin y x y = + 2 2 sin d d d y x y dx dx dx = + This can’t be solved for y . 2 2 cos dy dy x y dx dx = + 2 cos 2 dy dy y x dx dx - = ( 29 2 2 cos dy x y dx = - 2 2 cos dy x dx y = - This technique is called implicit differentiation. 1 Differentiate both sides w.r.t. x . 2 Solve for . dy dx
Background image of page 6
We need the slope. Since we can’t solve for y , we use implicit differentiation to solve for . dy dx Find the equations of the lines tangent and normal to the curve at .
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}