Unit 3 Calc-Pardy

Chain Rule

100

Differentiate: (x+1)²

2(x+1)

200

Differentiate: (4-x²)³

-6x(4-x²)²

300

Differentiate: cos(e^5x)

-5sin(e^5x)

400

Differentiate: tan²(e^2x+3)

4tan(e^2x+3)sec²(e^2x+3)

500

Differentiate: xcos(lnx)

cos(lnx)-sin(lnx)

Implicit Differentiation

100

Differentiate: 8x²+y²=10

y'=-8x/y

200

Differentiate: 5x²-xy-4y²=0

dy/dx=(10x-y)/(x+8y)

300

Differentiate: sinx+2cos2y=1

dy/dx=(cosx)/(4sin2y)

400

Differentiate: cos(xy)=xy

dy/dx=-y/x

500

find d²y/dx²: 5x²-2y²=4

d²y/dx²=-5/y³

Derivatives of Inverse Functions

100

find (f^-1)': f(x)=x³-1, y=7

[f^-1(7)]'=1/12

200

f(x)=(4/x)+12, find g'(10). g is the inverse of f

g'(10)=-1/16

300

find [f^-1(x)]': f(x)=x³+2x-1, y=2

[f^-1(x)]'=1/5

400

If f(3)=8 and f'(3)=5, what do you know about [f^-1(x)]'?

[f^-1(x)]'=1/5

500

Let f(x)=x³+x-2, and let g be the inverse function. Evaluate g'(0)

g'(0)=1/4

Derivative of Inverse Trig Functions

100

Differentiate: y=tan^-1(e^x)

y'=e^x/(1+e^2x)

200

Differentiate: y=cos^-1(x³)

y'=(-3x²)/sqrt(1-x⁶)

300

Differentiate: y=tan^-1(cosx)

y'=-sinx/(1+cos²x)

400

differentiate: y=ln|sin^-1x|

y'=1/((sin^-1x)(sqrt(1-x²)))

500

Differentiate: y=3arctan(e^3x)

y'=(9e^3x)/(1+e^6x)

Rivas Trivia

100

How many dogs does Mr. Rivas Have?

2 dogs

200

How many years has Mr. Rivas been teaching?

5 years

300

How many years has Mr. Rivas been at Central?

4 years

400

What is Mr. Rivas' conference period?

8th period

500

How old is Mr. Rivas?

29