Differentiation - The Multiplication Rule
There are also scenarios where we have two viable functions that multiply each other, and we would have to f
entire main function. This is also another scenario where differentiating from first principles may not exactly
The Multiplication Rule (differentiating two viable functions multiplyi
other…)
General Formulae:
If:
y = u ⋅ v
Then:
dy du dv
= v ⋅
+ u ⋅
dx dx dx
The Block Flow Diagram to Solving This:
y = u ⋅ v
↓
Split the entire function into two functions, u and v
↓
du
Take the derivative of each split function, so that you have u, v, an
dx
↓
Multiply the values according to the general formulae
↓
dy du dv
= v ⋅
+ u ⋅
dx dx dx
Example:
Let’s say we have this function:
y = 4x ⋅ sin(x)
Let’s split the function…
u v
y = 4x ⋅ sin(x)
There are also scenarios where we have two viable functions that multiply each other, and we would have to f
entire main function. This is also another scenario where differentiating from first principles may not exactly
The Multiplication Rule (differentiating two viable functions multiplyi
other…)
General Formulae:
If:
y = u ⋅ v
Then:
dy du dv
= v ⋅
+ u ⋅
dx dx dx
The Block Flow Diagram to Solving This:
y = u ⋅ v
↓
Split the entire function into two functions, u and v
↓
du
Take the derivative of each split function, so that you have u, v, an
dx
↓
Multiply the values according to the general formulae
↓
dy du dv
= v ⋅
+ u ⋅
dx dx dx
Example:
Let’s say we have this function:
y = 4x ⋅ sin(x)
Let’s split the function…
u v
y = 4x ⋅ sin(x)
