Implicit Differentiation

LVL 1

100

Find dy/dx if x² + y² =25 

-x/y

200

Find dy/dx if 3x + 2y=6

-3/2

300

Find dy/dx of xy=10

-y/x

400

Differentiate 2x + 3y² =12

-1/3y

500

Differentiate x³ + y³ =9

-x²/y²

LVL 2

100

Find the slope of the tangent to x²+xy =10 at the point (2,2)

dy/dx or y^' = -3

200

Find dy/dx if x/y= 5− x²

dy/dx= (-2xy² - y)/-x

300

Find dy/dx if x²− xy+ y²= 9

dy/dx= (-2x+y)/-x+2y

400

Find the equation of the tangent x/y + y=3 at (2,1)

y= x-1

500

Find the slope of the tangent line to x³+ y³ = 6xy, at the point (3,3)

-1

LVL 3

100

Find dy/dx if sin⁡(y)=x²

2x/cos(y)

200

Differentiate cos⁡(x+y)= xy.

(y + sin(x+y))/-sin(x+y)-x

300

Find y′ if sin⁡(x+y)= y²cos⁡x

(-y²sinx - cos(x+y))/ cos(x+y) - 2y(cosx)

400

Find dy/dx if e^y+yx= 4.

-y/e^y + x

500

Find the slope dy/dx for xe^y=x−y at (1,0).

dy/dx or y^' =0

LVL 4

100

Find dy/dx for y²+e^y= x²

2x/2y + e^y

200

Differentiate x/y + y² = 7

-y/ x- 2y³

300

Differentiate x³+e^y = xy²

dy/dx= (y²-3x²)/ e^y - 2xy

400

Find y^' of e^x+y = xy + 3

dy/dx= (y - e^x+y)/ e^x+y -x

500

^{Differentiate sin(xy) + cos(y)= x2}

(2x- ycos(xy))/ xcos(xy) - sin(y)

LVL 5

100

Find the equation of the tangent line sin(x + y)=x

y= 0

200

Find dy/dx for ln⁡(x+y)= xy.

y - 1/(x+y)/ 1/(x+y) - x

300

Find slope for x²y+ e^xy= 1 at (0,1)

dy/dx or y^'= 0

400

Differentiate tan⁡(xy)=x+y 

ysec²(xy) -1/-xsec²(xy) + 1

500

Differentiate cos⁡(xy)=x²+ y² at 

2x + ysin(xy)/-xsin(xy)-2y