How to Find the Derivative of cos(u) with Respect to x | Chain Rule Explained

d/dx cosu

To find the derivative of a function, we can use the chain rule

To find the derivative of a function, we can use the chain rule. In this case, we want to find the derivative of the function cos(u) with respect to x, which means u is a function of x.

Using the chain rule, the derivative of cos(u) with respect to x can be written as:

d/dx cos(u) = d/dx cos(u) * du/dx

The first term, d/dx cos(u), represents the derivative of cos(u) with respect to u, keeping in mind that u is a function of x. The second term, du/dx, represents the derivative of u with respect to x.

To find the derivative of cos(u), we can use the chain rule again. The derivative of cos(u) with respect to u is -sin(u). Multiplying this with du/dx, we get:

d/dx cos(u) = -sin(u) * du/dx

Therefore, the derivative of cos(u) with respect to x is -sin(u) times the derivative of u with respect to x.

Please note that without knowing the specific function u(x), we cannot simplify this further. If you provide the specific function u(x), we can proceed to find the final expression for the derivative.

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