Differentiation

Question 1

d/dx(cu)=?

Answer 1

cu’

Question 2

d/dx(u±v)=?

Answer 2

u’±v’

Question 3

d/dx(uv)=?

Answer 3

u’v+uv’

Question 4

d/dx(u/v)=?

Answer 4

(u’v−uv’)/v²

Question 5

d/dx(c)=?

Answer 5

0

Question 6

d/dx(uⁿ)=?

Answer 6

nuⁿ⁻¹u’

Question 7

d/dx(x)=?

Answer 7

1

Question 8

d/dx(∣u∣)=?

Answer 8

(u/∣u∣)u’

Question 9

d/dx(lnu)=?

Answer 9

u’/u

Question 10

d/dx(e^u)=?

Answer 10

e^u​u’

Question 11

d/dx(log_au)=?

Answer 11

u’/(lna)u

Question 12

d/dx(a^u)=?

Answer 12

(lna)a^uu’

Question 13

d/dx(sinu)=?

Answer 13

(cosu)u’

Question 14

d/dx(cosu)=?

Answer 14

−(sinu)u’

Question 15

d/dx(tanu)=?

Answer 15

(sec²u)u’

Question 16

d/dx(cotu)=?

Answer 16

−(csc²u)u’

Question 17

d/dx(secu)=?

Answer 17

(secutanu)u’

Question 18

d/dx(cscu)=?

Answer 18

−(cscucotu)u’

Question 19

d/dx(arcsinu)=?

Answer 19

u’/√(1−u²)

Question 20

d/dx(arccosu)=?

Answer 20

−u’/√(1−u²)

Question 21

d/dx(arctanu)=?

Answer 21

u’/(1+u²)

Question 22

d/dx(arccotu)=?

Answer 22

−u’/(1+u²)

Question 23

d/dx(arcsecu)=?

Answer 23

u²/(∣u∣√(u²−1))

Question 24

d/dx(arccscu)=?

Answer 24

−u²/(∣u∣√(u²−1))