Calculus

Question 1

(^d/_dx) y = sin(x)

Answer 1

y’= cos(x)

Question 2

(^d/_dx) y = cos(x)

Answer 2

y’ = -sin(x)

Question 3

(^d/_dx) y = tan(x)

Answer 3

y’ = sec²(x)

Question 4

(^d/_dx) y = sec(x)

Answer 4

y’ =sec(x)tan(x)

Question 5

(^d/_dx) y = csc(x)

Answer 5

y’ = -csc(x)cot(x)

Question 6

(^d/_dx) y = cot(x)

Answer 6

y’ = -csc²(x)

Question 7

(^d/_dx) y = e^x

Answer 7

y’ = e^x

Question 8

(^d/_dx) y = ln(x)

Answer 8

y’ = ¹/_x

Question 9

(^d/_dx) y = a^x

Answer 9

y’ = a^xln(a)

Question 10

(^d/_dx) y = log_a(x)

Answer 10

y’ = ¹/_{x ln(a)}

Question 11

What is the formula for ^d/_dx (^f(x)/_g(x))

Answer 11

= ^{(g(x)f’(x) - f(x)g’(x))}/_(g(x))²

Question 12

What is the formula for ^d/_dx (f(x)g(x))

Answer 12

= f(x)g’(x) + f’(x)g(x)

Question 13

what is the formula for ^d/_dx f(g(x))

Answer 13

= [f’(g(x))]g’(x)

Question 14

^d/_dx log_au

Answer 14

=^{u ‘}/_{u ln a}