Properties of Derivatives - Constant Multiple Rule
The constant multiple rule states that the derivative of a constant multiplied by a function is equal to the constant multiplied by the derivative of the function.
It can be expressed as:
(\displaystyle \frac{{d}}{{dx}}(cf(x)) = c \cdot \frac{{d}}{{dx}}f(x))
Where (c) is a constant.
Example of Constant Multiple Rule
Example: Find the derivative of the function (\displaystyle f(x) = 7x^2)
Example: Find the derivative of the function (\displaystyle f(x) = (2x+1)^3)
Step 1: Identify (f(x)) and (g(x))
(f(x) = x^3)
(g(x) = 2x+1)
Step 2: Find (f’(x)) and (g’(x))
(f’(x) = 3x^2)
(g’(x) = 2)
Step 3: Apply the chain rule formula
(\displaystyle \frac{{d}}{{dx}}((2x+1)^3) = f’(g(x))\cdot g’(x) = 3(2x+1)^2 \cdot 2)
Sure! Here are slides 21 to 30 on the topic of “Derivatives - Examples of Quotient Rule”:
Quotient Rule - Recap
The quotient rule is used to find the derivative of a function that is expressed as the quotient of two other functions.