Derivatives Formulas

Question 1

d/dx sinx

Answer 1

cosx

Question 2

d/dx cosx

Answer 2

-sinx

Question 3

d/dx tanx

Answer 3

sec²x

Question 4

d/dx cscx

Answer 4

-cscxcotx

Question 5

d/dx secx

Answer 5

secxtanx

Question 6

d/dx cotx

Answer 6

-csc²x

Question 7

d/dx arcsinx

Answer 7

1/(root(1-x²))

Question 8

d/dx arccosx

Answer 8

-1/root(1-x²)

Question 9

d/dx arctanx

Answer 9

1/(1+x²)

Question 10

d/dx arccscx

Answer 10

-1/(|x|root(x²-1)

Question 11

d/dx arcsecx

Answer 11

1/(|x|root(x²-1)

Question 12

d/dx arccotx

Answer 12

-1/(1+x²)

Question 13

d/dx lnx

Answer 13

1/x

Question 14

d/dx 1/x

Answer 14

-1/x²

Question 15

d/dx a^x

Answer 15

a^xlna

Question 16

d/dx xⁿ

Answer 16

nx^n-1

Question 17

d/dx f(x)g(x)

Answer 17

f (x)g(x) + g (x)f(x)

Question 18

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

Answer 18

(f(x) * g(x)- f(x) * g(x))/g(x)^2

Question 19

f(g(x))’

Answer 19

g(x)’ * f ‘ (g(x))

Question 20

2 definitions of derivative

Answer 20

f’(x) = lim (f(x+h)-f(x))/h as h approaches infinity

f’(c) = lim (f(x)-f(c))/(x-c) as x approaches c

Question 21

what is acceleration?

Answer 21

x’‘(t)

Question 22

what is velocity?

Answer 22

x’(t)

Question 23

when is speed increasing?

Answer 23

when signs of acceleration and velocity is the same

Question 24

when is speed decreasing

Answer 24

when signs of velocity and acceleration is not the same