Limits And Derivatives

Question 1

d|dx(c)=?

Answer 1

0

Question 2

d|dx(x^n)=?

Answer 2

nx^(n-1)

Question 3

d|dx(e^x)=?

Answer 3

e^x

Question 4

d|dx[f(x)+g(x)]=?

Answer 4

f’(x)+g’(x)

Question 5

d|dx[f(x)-g(x)]=?

Answer 5

f’(x)-g’(x)

Question 6

d|dx[f(x)*g(x)]=?

Answer 6

f’(x)g(x)+f(x)g’(x)

Question 7

d|dx[N(x)/D(x)]=?

Answer 7

[N’(x)D(x)]-[D’(x)N(x)]/[D(x)]^2

Question 8

d|dx(cosx)=?

Answer 8

-sinx

Question 9

d|dx(sinx)=?

Answer 9

cosx

Question 10

d|dx(tanx)=?

Answer 10

sec^2x

Question 11

d|dx(cotx)=?

Answer 11

-csc^2x

Question 12

d|dx(secx)=?

Answer 12

secxtanx

Question 13

d|dx(cscx)=?

Answer 13

-cscxcotx

Question 14

d|dx{c[f(x)]}=?

Answer 14

C*f’(x)

Question 15

What is the chain rule?

Answer 15

d|dx{f[g(x)]}=f’[g(x)]*g’(x)}

Question 16

f’(x)=?

Answer 16

lim ➡️ 0

f(x+h)-f(x)/h

Question 17

What is the limit as theta approaches 0 of sin(theta)/theta

Answer 17

1️⃣

Question 18

What is the limit as theta approaches 0 of cos(theta)-1/theta

Answer 18

0️⃣

Question 19

d|dx(x)=?

Answer 19

1