Understanding the Derivative of y = cosx Using dy/dx cosx

dy/dx cosx

The expression “dy/dx” represents the derivative of a function “y” with respect to another variable “x”

The expression “dy/dx” represents the derivative of a function “y” with respect to another variable “x”. In this case, “cosx” represents the function “y = cosx”. So, when we write “dy/dx cosx”, we are asking for the derivative of the cosine function with respect to the variable “x”.

To find the derivative of “y = cosx”, we can use the chain rule. The chain rule states that if we have a composite function, we can find its derivative by multiplying the derivative of the outer function with the derivative of the inner function.

In this case, the outer function is “cosx” and the inner function is “x”. The derivative of the outer function “cosx” with respect to “x” is given by “-sinx”. Since the derivative of “x” with respect to “x” is simply 1, we can apply the chain rule as follows:

dy/dx = (dy/dx) cosx = (-sinx) * (dx/dx) = -sinx

Hence, the derivative of “y = cosx” with respect to “x” is “-sinx”.

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