Dx {tan x}=?
To find the derivative of the tangent function, Dx {tan x}, we can use the quotient rule
To find the derivative of the tangent function, Dx {tan x}, we can use the quotient rule.
The tangent function can be written as tan x = sin x / cos x.
Let’s differentiate sin x and cos x separately first:
Dx {sin x} = cos x
Dx {cos x} = -sin x
Now, we can apply the quotient rule:
Dx {tan x} = (Dx {sin x} * cos x – sin x * Dx {cos x}) / (cos x)^2
Substituting the values we found earlier:
Dx {tan x} = (cos x * cos x – sin x * (-sin x)) / (cos x)^2
= (cos^2 x + sin^2 x) / (cos x)^2
= 1 / (cos x)^2
Therefore, the derivative of the tangent function is Dx {tan x} = 1 / (cos x)^2.
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