derivative of tan^2(x)
2tan(x)sec^2(x)
To find the derivative of tan²(x), we can use the chain rule and the power rule.
Let y = tan²(x)
Then
y = tan(x) * tan(x)
Now take the derivative of both sides with respect to x:
dy/dx = d/dx (tan(x) * tan(x))
Using the product rule, we get:
dy/dx = tan(x) * sec²(x) + sec²(x) * tan(x)
Using the identity 1 + tan²(x) = sec²(x), we can simplify this to:
dy/dx = 2 tan(x) sec²(x)
Therefore, the derivative of tan²(x) is 2 tan(x) sec²(x).
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