d/dx [ tan(x) ]
To find the derivative of the function f(x) = tan(x), we need to use the chain rule
To find the derivative of the function f(x) = tan(x), we need to use the chain rule.
The chain rule states that the derivative of a composite function is equal to the derivative of the outer function times the derivative of the inner function.
In this case, the outer function is tan(x), and the inner function is x.
So, let’s go step by step:
1. Begin by finding the derivative of the outer function, which is tan(x). The derivative of tan(x) can be found using the trigonometric identity:
d/dx [tan(x)] = sec^2(x)
2. Next, find the derivative of the inner function, which is x. The derivative of x with respect to x is simply 1.
3. Now, we multiply the two derivatives together:
d/dx [tan(x)] = sec^2(x) * 1
Simplifying the expression, we have:
d/dx [tan(x)] = sec^2(x)
So, the derivative of tan(x) with respect to x is sec^2(x).
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