Differentiate Rules

Question 1

Constant Rule: d/dx [C]

Answer 1

0

Question 2

Power Rule: d/dx [x^(n)]

Answer 2

nx^(n-1)

Question 3

Product Rule: d/dx [f(x)g(x)]

Answer 3

d/dx [f(x)] (g(x)) + d/dx [g(x)] (f(x))

Question 4

Quotient Rule: d/dx [f(x)/g(x)]

Answer 4

(d/dx [f(x)] (g(x)) - f(x) (d/dx [g(x)]) / (g(x))^2

Question 5

Exponential Rule: d/dx [e^(x)]

Answer 5

e^x

Question 6

lim (sin(x))/(x)=?

x->0

Answer 6

1

Question 7

lim (cos(x)-1)/(x)=?

x->0

Answer 7

0

Question 8

Trig Function: d/dx [sin(x)]

Answer 8

cos(x)

Question 9

Trig Function: d/dx [cos(x)]

Answer 9

-sin(x)

Question 10

Trig Function: d/dx [tan(x)]

Answer 10

(sec(x))^2

Question 11

Trig Function: d/dx [csc(x)]

Answer 11

(-csc(x))(cot(x))

Question 12

Trig Function: d/dx [sec(x)]

Answer 12

(sec(x))(tan(x))

Question 13

Trig Function: d/dx [cot(x)]

Answer 13

(-csc(x))^2

Question 14

Log Function: d/dx [log_(a) (X)]

Answer 14

1/(x)(ln (a))

Question 15

Log Function: d/dx [ln (x)], where x>0

Answer 15

1/x

Question 16

Exponential Function: d/dx [a^(x)], where “a” is a base number

Answer 16

(a^(x))(ln(a))

Question 17

Inverse Trig Function: d/dx [(sin(x))^(-1)]

Answer 17

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

Question 18

Inverse Trig Function: d/dx [(cos(x))^(-1)]

Answer 18

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

Question 19

Inverse Trig Function: d/dx [(tan(x))^(-1)]

Answer 19

1/(1+x^(2))

Question 20

Inverse Trig Function: d/dx [(cot(x))^(-1)]

Answer 20

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

Question 21

Inverse Trig Function: d/dx [(sec(x))^(-1)]

Answer 21

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

Question 22

Inverse Trig Function: d/dx [(csc(x))^(-1)]

Answer 22

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