d/dx arccos
To find the derivative of arccos(x) with respect to x, we can use the chain rule
To find the derivative of arccos(x) with respect to x, we can use the chain rule. The chain rule states that if we have a function f(g(x)), then its derivative is given by f'(g(x)) multiplied by g'(x).
In this case, let’s assign g(x) = x and f(u) = arccos(u). Therefore, f(g(x)) = arccos(x).
Now, we need to find the derivatives of f(u) and g(x).
The derivative of f(u) = arccos(u) with respect to u is given by:
f'(u) = -1/√(1 – u^2).
The derivative of g(x) = x with respect to x is simply 1.
Then, using the chain rule, the derivative of arccos(x) with respect to x can be calculated as follows:
(d/dx) arccos(x) = f'(g(x)) * g'(x)
= (-1/√(1 – x^2)) * 1
= -1/√(1 – x^2).
Therefore, the derivative of arccos(x) with respect to x is -1/√(1 – x^2).
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