Derivative Rules

Question 1

Constant Rule

Answer 1

f(x) = C -> f’(x) = 0
Essentially, the derivative of any constant is 0.

Question 2

Sum Rule

Answer 2

f(x) = g(x) + h(x) -> f’(x) = g’(x) + h’(x)

Question 3

Product Rule

Answer 3

f(x) = g(x).h(x) -> f’(x) = g’(x) . h(x) + h’(x) . g(x)

Question 4

Chain Rule

Answer 4

f(x) = g(h(x)) -> f’(x) = g’(h(x)) . h’(x)
Lets say we have (2x)^2
We can rewrite this as 2 . 2x . 2, since (ax)^b becomes b(ax)^b-1.

Question 5

Power Rule

Answer 5

f(x) = x^t -> f’(x) = t . x^t-1

Question 6

Sin, Cos and Tan Rules

Answer 6

sinx -> cosx
-sinx -> -cosx
cosx -> -sinx
-cosx -> sinx
tanx -> (sin x)^2 + (cos)^2 / (cos x)^2 = sec^2 (x)
-tanx -> -sec^2 (x)

Question 7

Exponential Rule

Answer 7

f(x) = e^u -> f’(x) = e^u . ‘u
For example, d/dx[e^x] -> e^x . 1 = e^x

Question 8

Natural Log Rule

Answer 8

f(x) = ln(u) -> u’/u

Question 9

Quotient Rule

Answer 9

f(x) = g(x) / h(x) -> f’(x) = (g’(x) . h(x)) - (g(x) . h’(x)) / h(x) . h(x)

Question 10

X rules (2x, x)

Answer 10

Cx -> C, where C is a constant
x -> 1

Question 11

Square Root

Answer 11

f(x) = sqrt(4x + 5)
f’(x) = ‘(4x+5) / 2 * sqrt(4x + 5)