Evaluating a Derivative

Question 1

y=c

Answer 1

y’=0

Question 2

y=x^n

Answer 2

y’=nx^(n-1)

Question 3

y=e^x

Answer 3

y’=e^x

Question 4

Product Rule

Answer 4

d/dx(fg)=fg’+gf’

Question 5

Quotient Rule

Answer 5

d/dx(f/g)=(gf’-fg’)/g^2

Question 6

Chain Rule

Answer 6

d/dx(f(g)=f’(g)g’

Question 7

Exponential Rule

Answer 7

d/dx(n^u)=n^uln(n)u’

Question 8

Equation of a Tangent Line

Answer 8

1. Find f’(x)
2. Evaluate f’(x) at c, where (c,f(c))
3. Point-Slope form equation: y-y₁=m(x-x₁)
   -y₁=f(c)
   -x₁=c
   -m=f’(c)

Question 9

y=sin(x)

Answer 9

y’=cos(x)

Question 10

y=cos(x)

Answer 10

y’=-sin(x)

Question 11

y=tan(x)

Answer 11

y’=sec^2(x)

Question 12

y=cot(x)

Answer 12

y’=-csc^2(x)

Question 13

y=sec(x)

Answer 13

y’=sec(x)tan(x)

Question 14

y=csc(x)

Answer 14

y’=-csc(x)cot(x)

Question 15

y=sin^-1(x)

Answer 15

y’=1/√(1-x^2)*x’

Question 16

y=cos^-1(x)

Answer 16

y’=-1/√(1-x^2)*x’

Question 17

y=tan^-1(x)

Answer 17

y’=1/(1-x^2)*x’

Question 18

y=cot^-1(x)

Answer 18

y’=-1/(1+x^2)*x’

Question 19

y=sec^-1(x)

Answer 19

y’=1/(x√(x^2-1))*x’