implicit differentiation

fun facts

100

The opposite of an implicitly defined equation.

What is an explicitly defined equation?

200

The name of an implicitly defined equation.

What is an implicit formula?

300

The inventor of implicit differentiation.

What is Isaac Newton and/or Gottfried Wilhelm Leibniz?

400

The first step of implicit differentiation

What is differentiating both sides of the equation with respect to x?

500

The second step of implicit differentiation

What is applying the chain rule?

implicit or explicit?

100

x³+xy²+y=1

What is an implicitly defined equation?

200

y=-3x²+2x+4

What is an explicitly defined equation?

300

5x+x³+2x⁸=y

What is explicit differentiation?

400

x²+y²=6x²

What is an implicitly defined equation?

500

y²=(x-2)/(3-x)

What is implicit differentiation?

trig functions

100

find dy/dx

x=sin(y)

sec(y)=dy/dx

200

find dy/dx

x=sec(y)

cos(y)cot(y)=dy/dx

300

find dy/dx

x=cos(y)

-cos(x)=dy/dx

400

find dy/dx

x=tan(y)

cos^2(y)=dy/dx

500

find dy/dx

x²=sin(y)

2x/cos(y)=dy/dx

mild

100

x³+y³=18xy

(6y-x²)/(y²-6x)

200

2y³+4x²-y=x⁶

y'=(6x⁵-8x)/(6y²-1)

300

find the equation of the tangent line

x⁴+y²=3 at (1, -2^(1/2))

y'=-2x³/y

400

x/y³=1

y'=(1/3)x^-2/3

500

x²+y³=4

y'=-(2/3)x(4-x²)^-2/3

burn your mouth off

100

7y²+sin(3x)=12-y⁴

y'=(-3cos(3x))/(14y+4y³)

200

find the slope of the tangent line to x²+y²=y+5y+14 at (3,1)

1.5

300

tan(x²y⁴)=3x+y²

y'=(3-2xy⁴sec²(x²y⁴))/(4x²y³sec²(x²y⁴)-2y)

400

e^x-sin(y)=x

y'=(e^x-1)sec(y)

500

cos(x²+2y)+xe^{y^2}=1

y'=(2xsin(x²+2y)-e^{y^2})/(2yxe^{y^2}-2sin(x²+2y))