Calculus AB Trig Derivative Review

Trig Formulas

100

d(cosu)=

-sinu*du

200

d(cotu)=

-csc^2(u)*du

300

d(cscu)=

-cscu*cotu*du

400

d(tanu)=

sec^2(u)*du

500

d(secu)=

secu*tanu*du

Trig Derivatives

100

y=sin(2x), dy/dx=

2cos (2x)

200

y=tan(3-x), dy/dx=

-sec^2(3-x)

300

y=csc(x^2), dy/dx=

-2xcsc(x^2)cot(x^2)

400

y=sec(pi+3x), dy/dx=

3sec(pi+3x)tan(pi+3x)

500

y=cot(x/2), dy/dx=

-1/2csc^2(x/2)

Trig Rules:pwr,prdct,qtnt,imp diff,final jprdy

100

y=sec^2x, dy/dx=

2secxsecxtanx or2sec^2xtanx

200

y=cotxsecx, dy/dx=

cotxsecxtanx-secxcsc^2x or secx-secxcsc^2x

300

y=sinx/cosx, dy/dx=

(cos^2x+sin^2x)/cos^2x or 1/cos^2x orsec^2x

400

x=cscy, dy/dx=

-1/(cscycoty

500

Final Jeopardy.  With your calculator, find the derivative of:

  xy+secy=1/4

(-y(cos(y))^2)/(x(cos(y))^2+sin(y)

Calculator Allowed

100

Find the Equation of the Normal line at  

x=pi/3

for f(x)=cos(x)

y=(2sqrt3*x)/3-(4pisqrt3-9)/18 or1.155x-0.709

200

Find the Equation of the Tangent Line at 

x=pi

for f(x)=tan(x)

y=x-3.142 or y=x-pi

300

If f(x)=sec(3x), find

f'(pi)

0

400

If f(x)=csc(2x), find:

f'(pi/6)

-1.333 or 

-4/3

500

If

f(x)=sqrtsinx

Find

f'(pi/4)

0.420 or 

2^(3/4)/4