Remember that the gradient of a straight line is m. The tangent to the line is the line itself, so the gradient of tangent is m everywhere along the line.
So if .
For a horizontal line in the form y=k, the gradient is zero.
So if .
In short, we could say that:
A more general way of writing the rule is:
Also, if there are several terms in an expression, we differentiate each one separately. We can write this as a rule:
Differentiate each function:
4. If , evaluate
5. Differentiate with respect to r.
Composite Function Rule
A composite function is a function composed of two or more other functions. For example, is made up of a function where .
To differentiate a composite function, we need to use the result:
The derivative of a composite function is the product of two derivatives. One is the derivative of the function inside the brackets. The other is the derivative of the whole function.