Derivative of cosine
The derivative of the cosine of a function is equal to the sine of that function, multiplied by the derivative of the same and by minus 1, that is, it changes from the positive sign to the negative sign or vice versa.
We must remember that the derivative is a mathematical function that is defined as the rate of change of one variable with respect to another. That is, by what percentage one variable increases or decreases when another has also increased or decreased.
The derivative of a function is defined as follows:
Let's quickly look at the following example:
Another concept that we must remember is that of cosine. This is a trigonometric function that can be calculated on a right triangle. Thus, the cosine of an angle x is equal to the quotient of the adjacent leg and the hypotenuse.
It is worth mentioning that a right triangle is one where one of the angles is right (or 90º), and the other two are acute angles. Thus, the hypotenuse is the side of greatest measure and is opposite the right angle. Meanwhile, the other two sides are called legs.
Examples of derivatives of cosine
We are going to calculate the derivative of the following function:
Now, let's look at a second example: