...of logs & exponentials
...of trig functions
...of inverse functions
...of inverse trig functions
...implicitly!
100
Find f'(x):
f(x)=e^(4x)
4e^(4x)
100
Find f'(x):
f(x)=sin(2x)
2cos(2x)
100
Let f(x)=x^3+2x-1 and let g be the inverse function of f. Notice that f(2)=11.
Find (f-1)'(11)
1/14
100
Find f'(x):
f(x)=cos^-1(x)
-1/sqrt(1-x^2)
100
Find dy/dx in terms of x and y:
2x^3=2y^2+5
dy/dx=(3x^2)/(2y
200
Find f'(x):
f(x)=lne
0
200
Find f'(x):
f(x)=cos(x^2)
-2xsin(x^2)
200
Let g and h be inverse functions.
The following table lists a few values of g, h, and h'.
Find (g-1)'(0).
-1
200
Find f'(x):
f(x)=sin^-1(2x^2)
(4x)/sqrt(1-4x^4
200
Find dy/dx in terms of x and y:
5y^2=2x^3-5y
dy/dx=(6x^2)/(10y+5)
300
Find f'(x):
f(x)=ln(sinx)
(cosx)/(sinx)
cotx
300
Find f'(x):
f(x)=tan(3x^2)
6xsec^2(3x^2)
300
Let g(x)=x^5+3x and let h be the inverse function of g. Notice that g(1)=4.
1/8
300
Find f'(x):
f(x)=(tan^-1(5x))^2
10/(25x^2+1)
300
Find dy/dx in terms of x and y:
3x^2y^2=4x^2-4xy
dy/dx=(4x-2y-3xy^2)/(3x^2y+2x)
400
Find f'(x):
f(x)=ln(x^3e^x)
3/x+1
400
Find f'(x):
f(x)=cos^2(x^2-2x)
-2(2x-2)cos(x^2-2x)sin(x^2-2x)
400
Let f and g be inverse functions.
The following table lists a few values of f, g, and f'.
Find g'(2).
12
400
Find f'(x):
f(x)=arccsc(4x^2)
-(8x)/(abs(4x^2)sqrt(16x^4-1) =
-2/(xsqrt(16x^4-1)
400
Find dy/dx in terms of x and y:
3x^2+3=ln(5xy^2)
dy/dx=(6x^2y-y)/(2x)
500
*If you don't remember the formula, use logarithmic differentiation!
Find f'(x):
f(x)=2^(3x)
3(2^(3x)ln2)
500
Find f'(x):
f(x)=csc(sinx)
-csc(sinx)cot(sinx)cosx
500
Find the equation of the tangent line to the inverse of f(x) at x=10.
f(x)=x^3+7x+2
y-1=1/10(x-10)
500
Find f'(x):
f(x)=arcsec(3x^5+x)
(15x^4+1)/(abs(3x^5+x)sqrt((3x^5+x)^2-1)
500
Find dy/dx in terms of x and y:
sin(2x^2y^3)=3x^3+1
dy/dx=(9x-4y^3cos(2x^2y^3))/(6xy^2cos(2x^2y^3)