Differentiation (trig, exponentials and logs)

Question 1

derivative of sinx

Answer 1

cos x

Question 2

derivative of cosx

Answer 2

-sinx

Question 3

derivative of tanx

Answer 3

sec^2x

Question 4

derivative of sin(ax+b)

Answer 4

acos(ax+b)

Question 5

derivative of cos(ax+b)

Answer 5

-asin(ax+b)

Question 6

derivative of tan(ax+b)

Answer 6

asec^2(ax+b)

Question 7

derivative of logex

Answer 7

1/x

Question 8

derivative of logef(x)

Answer 8

f’(x)/f(x)

derivative over original

Question 9

derivative of (a^x)

Answer 9

(lna)a^x

ln of the function times by original function

Question 10

derivative of (a^f(x))

Answer 10

(lna)f’(x)a^f(x)

ln of function times by derivative of function times by original function

Question 11

derivative of logax

Answer 11

1/xlna

1 over x times ln of base a

Question 12

derivative of logaf(x)

Answer 12

f’(x)/(lna) f(x)

derivative of f(x) over ln of base a times by original f(x)

Question 13

derivative of e^f(x)

Answer 13

f’(x)e^f(x)

derivation of f(x) times by the original function