Derivative rules

Question 1

(d/dx) (a^x)

Answer 1

a^x * lnx

Question 2

(d/dx)(x^n)

Answer 2

nx^n-1

Question 3

(d/dx)(F(x)*g(x))

Answer 3

(f’(x))(g(x)) + (f(x))(g’(x))

Question 4

(d/dx)f(x))/g(x)

Answer 4

(low)(d’high) - (high)(d’low) / (low^2)

Question 5

(d/dx)(ln(x))

Answer 5

1/x, x>0

Question 6

(d/dx)(ln|x|)

Answer 6

1/x, x /=0

Question 7

(d/dx)(e^x)

Answer 7

e^x

Question 8

(d/dx) (c*f(x))

Answer 8

c*f’(x)

Question 9

(d/dx)log(a)(x)

Answer 9

1/(x)ln(a)

Question 10

(d/dx)(sin(x))

Answer 10

cos(x)

Question 11

(d/dx)(cos(x))

Answer 11

-sin(x)

Question 12

(d/dx)(tan(x))

Answer 12

sec^2(x)

Question 13

(d/dx)(csc(x))

Answer 13

-csc(x)*cot(x)

Question 14

(d/dx)(sec(x))

Answer 14

sec(x)*tan(x)

Question 15

(d/dx)(cot(x))

Answer 15

-csc^2(x)

Question 16

(d/dx)(sin^-1(x))

Answer 16

1/sqrt. (1-x^2)

Question 17

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

Answer 17

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

Question 18

(d/dx)(tan^-1(x))

Answer 18

1/(1+x^2)

Question 19

(d/dx)(sqrt. (x))

Answer 19

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

Question 20

(d/dx)(cbrt. (x))

Answer 20

(1/3)x^(-2/3)