Derivative of sin(u) with respect to x using the chain rule

d/dx sinu

The expression “d/dx sinu” represents the derivative of the function sin(u) with respect to the variable x

The expression “d/dx sinu” represents the derivative of the function sin(u) with respect to the variable x. To compute this derivative, we can use the chain rule of differentiation.

Chain Rule:
The chain rule states that if we have a composite function y = f(g(x)), then the derivative of y with respect to x, written as dy/dx, is given by dy/dx = f'(g(x)) * g'(x).

Using the chain rule, let’s find the derivative of sin(u) with respect to x.

Given: y = sin(u), where u is a function of x.

To find dy/dx, we need to find dy/du and du/dx.

1. Find dy/du:
The derivative of sin(u) with respect to u is given by cos(u). So, dy/du = cos(u).

2. Find du/dx:
We are given that u is a function of x, so we need to find du/dx. The exact form of u(x) is not provided, so we cannot determine this derivative without more information.

Combining steps 1 and 2:
Using the chain rule, dy/dx = (dy/du) * (du/dx) = cos(u) * du/dx.

Without knowing the specific form of u(x), we cannot simplify this expression further.

In conclusion, the derivative of sin(u) with respect to x, denoted as d/dx sinu, is given by cos(u) * du/dx, where du/dx depends on the specific function u(x).

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