Differentiation ;)

Question 1

y = x^n

Answer 1

dy/dx = nx^n-1

Question 2

y = [f(x)]^n

Answer 2

dy/dx = n [f(x)]^n-1 x f’(x)

Question 3

y = sinx

Answer 3

dy/dx = cos x

Question 4

y = sin(f(x))

Answer 4

dy/dx = cos(f(x)) x f’(x)

Question 5

y = cos x

Answer 5

dy/dx = - sinx

Question 6

y = - sinx

Answer 6

dy/dx = - cos x

Question 7

y = - cosx

Answer 7

dy/dx = sinx

Question 8

y = tanx

Answer 8

dy/dx = sec^2x

Question 9

y = tan(f(x))

Answer 9

dy/dx = sec^2(f(x)) x f’(x)

Question 10

y = sec(f(x))

Answer 10

dy/dx = sec(f(x)) tan (f(x)) x f’(x)

Question 11

y = cot(f(x))

Answer 11

dy/dx = -cosec^2(f(x)) x f’(x)

Question 12

y = cosec(f(x))

Answer 12

dy/dx = -cosec(f(x)) cot(f(x)) x f’(x)

Question 13

y = e^x

Answer 13

dy/dx = e^x

Question 14

y= e^f(x)

Answer 14

dy/dx = e^f(x) x f’(x)

Question 15

y = a^x

Answer 15

dy/dx = a^x x ln(a)

Question 16

y = a^f(x)

Answer 16

dy/dx = a^f(x) x ln(a) x f’(x)

Question 17

y = ln(x)

Answer 17

dy/dx = 1 / x

Question 18

y = ln(f(x))

Answer 18

dy/dx = f’(x) / f(x)

Question 19

PRODUCT RULE

Answer 19

dy/dx = uv’ + vu’

Question 20

QUOTIENT RULE

Answer 20

dy/dx = (vu’ - uv’) / v^2