Formulas

Question 1

dy/dx(x^n) = nx^n-1

Answer 1

Power Rule

Question 2

dy/dx(e^x) = e^x

Answer 2

Base e

Question 3

dy/dx(f(x)g(x)) = f’(x)g(x)+f(x)g’(x)

OR f(x)g’(x)+f’(x)g(x)

Answer 3

Product Rule

Question 4

dy/dx(f(x)/g(x)) = f’(x)g(x)-f(x)g’(x)/[g(x)]^2

Answer 4

Quotient Rule

Question 5

f(g(x))

f’(g(x))(g’(x))

Answer 5

Chain Rule

Question 6

lim = sin(x)/(x) = 1 lim = cos(x)-1/(x) = 0 lim = (x)/sin(x)=1
x ->0 x ->0 x->0

Answer 6

Limits

Question 7

Derivative of Trig Functions

dy/dx(sin (x)) = ______

Answer 7

cos(x)

Question 8

Derivative of Trig Functions

dy/dx(cos(x)) = _____

Answer 8

-sin(x)

Question 9

Derivative of Trig Functions

dy/dx(tan(x)) = _____

Answer 9

sec^2(x)

Question 10

Derivative of Trig Functions

dy/dx(sec(x)) = __

Answer 10

sec(x)tan(x)

Question 11

Derivative of Trig Functions

dy/dx(cot(x)) = __

Answer 11

-csc^2(x)

Question 12

Derivative of Trig Functions

dy/dx(csc(x)) = __

Answer 12

-csc(x)cot(x)

Question 13

dy/dx(cos^(-1)(x))

Answer 13

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

Question 14

dy/dx(cot^(-1)(x))

Answer 14

-1/(1+x^2)

Question 15

csc^(-1)(x)

Answer 15

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