d/dx sinx
To find the derivative of the function f(x) = sin(x) with respect to x, denoted as d/dx sin(x), we will use the chain rule
To find the derivative of the function f(x) = sin(x) with respect to x, denoted as d/dx sin(x), we will use the chain rule.
The chain rule states that if we have a composite function g(f(x)), where g(x) and f(x) are differentiable, then the derivative of g(f(x)) with respect to x is given by g'(f(x)) * f'(x).
In this case, the function sin(x) can be viewed as the composition of two functions: f(x) = sin(x) and g(x) = x. Applying the chain rule, we have:
d/dx(sin(x)) = d/dx(g(f(x))) = g'(f(x)) * f'(x)
Let’s calculate the derivatives separately:
f(x) = sin(x)
The derivative of sin(x) with respect to x is cos(x), so f'(x) = cos(x).
g(x) = x
The derivative of x with respect to x is 1, so g'(x) = 1.
Now, substitute these values into the chain rule:
d/dx(sin(x)) = g'(f(x)) * f'(x) = 1 * cos(x) = cos(x)
Therefore, the derivative of sin(x) with respect to x is cos(x).
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