Derivative Rules

Question 1

d/dx x^n

Answer 1

nx^n-1

Question 2

d/dx f(g(x))

Answer 2

f’(g(x)) . g’(x)

Question 3

d/dx f(x)g(x)

Answer 3

f(x).g’(x) + g(x).f’(x)

Question 4

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

Answer 4

[g(x).f’(x)-f(x).g’(x)]/[g(x)]^2

Question 5

d/dx sinx

Answer 5

cosx

Question 6

d/dx cosx

Answer 6

-sinx

Question 7

d/dx tanx

Answer 7

sec^2(x)

Question 8

d/dx cscx

Answer 8

-cscx.cotx

Question 9

d/dx secx

Answer 9

secx.tanx

Question 10

d/dx cotx

Answer 10

-csc^2(x)

Question 11

d/dx e^x

Answer 11

e^x

Question 12

d/dx a^x

Answer 12

a^x ln(a)

Question 13

d/dx lnx

Answer 13

1/x

Question 14

d/dx log(a)x

Answer 14

1/(x ln a)

Question 15

d/dx sin^(-1)x

Answer 15

1/(sqrt 1-x^2)

Question 16

d/dx cos^(-1)x

Answer 16

-1/(sqrt 1-x^2)

Question 17

d/dx cot^(-1)x

Answer 17

1/(1+x^2)

Question 18

If f(x) and g(x) are inverses, then g’(x)

Answer 18

1/f’(g(x))

Question 19

If f(x) and g(x) are inverses, then f’(x)

Answer 19

1/g’(f(x))