Derivatives Of Cos

What is derivative?

What is derivative?

Derivative means differentiation of any trigonometric function and also for inverse trigonometric function. Derivative cos means one time differentiation of any cos function. it is a mathematical process to derive derivative cos. To find derivative cos we have to differentiate the cos function with respect to variable. That means the rate at which cos function changes with respect to given variable.

Another approach to find the derivative is by using slope criteria. The derivative is the slope of a line tangent to the point. The derivatives are very useful in finding slope of any function.

For example, derivative=slope=rat of change. If y is equal to function of cos then derivative of cos can be written as y or (y-prime) or dy/dx.

Rule and Methods of derivative

We can find derivative of any trigonometric function by using rules such as Sumrule, Differencerule, Product rule, Quotientrule and Chain rule. Using these five rules, we can differentiate most of the cases where y is an explicit function of x.

Now various methods used to find derivatives are Differentiation by substitution, Implicitdifferentiation, Logarithmic differentiationand Parametric differentiation.

Lets understand the concept further by a couple of examples.

How to find derivative of cosx

To calculate derivative cosx we first differentiate the trigonometric function only one time. In this process the calculating function is cosx. By differentiating we get negative of (sinx) which means the rate of change of cosx at a particular given point x. finally the result of derivative cosx is sinx with negative sign.

d/dx(cosx)= -sinx

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How to find derivative of cos 2x

This is a chain rule type differentiation. To calculate derivative of cos2x, we find first derivative cosx which we get negative of (sinx). But here we have to calculate the term which is inside means 2x and the derivative of 2x is 2. This process is because of chain rule. Finally the result of derivative of cos2x, we get (2sin2x) with negative sign.

d/dx (cos2x)= -2sin2x

What is derivative of cos 2 X?

For finding the value of derivative of cos 2 X we differentiation individually cos2 X and 2 X. it is based on chain rule. By differentiating we get the value of derivative of cos2 X is (2sin2 X) with negative sign.

Applications of derivatives

There are only two areas where derivatives are used as listed follows:

1. Increasing and decreasing function

2. Maxima and minima

by: Omkar Nayak

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