Unit Two: Derivatives

Question 1

Definition of derivatives

Answer 1

(f(X+change inX) - f(x))/change in x as the limit of change in X goes to 0

Question 2

Y’ {f(x)/g(x)}

Answer 2

Low d high minus high d low all over low low

(g(x)f’(x) - f(x)g’(x))/(g(x))^2

Question 3

Y’ {f(x)*g(x)}

Answer 3

f’(x)g(x) + f(x)g’(x)

Question 4

Y’ {c*f(x)}

Answer 4

c *f’(x)

Question 5

Y’ {c}

Answer 5

0

Question 6

Y’ {x^n}

Answer 6

n*x^(n-1)

Question 7

Y’ {f(x) +/- g(x)}

Answer 7

f’(x) +/- g’(x)

Question 8

Y’ {sin x}

Answer 8

cos x

Question 9

Y’ {cos x}

Answer 9

-sin x

Question 10

Y’ {tan x}

Answer 10

sec^2 x

Question 11

Y’ {csc x}

Answer 11

-csc x *cot x

Question 12

Y’ {cot x}

Answer 12

-csc^2 x

Question 13

Y’ {sec x}

Answer 13

secx * tanx

Question 14

Y’ [f(g(x))]

Answer 14

F’ (g(x)) * g’(x)

Question 15

What is the difference between the explicit and implicit form?

Answer 15

E- the function is solved for y

I- the function is not solved for y (includes the derivatives of all variables)