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MathCalculus

Derivative of Trigonometric Functions: Differentiate csc x + x tan x

The sum and product rules give f′(x) = −csc x cot x + tan x + x sec²x on the original function's domain.

Question

Find the derivative of

f(x)=csc⁡x+xtan⁡x.f(x)=\csc x+x\tan x.

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Evidence boundary

The derivative is valid only where the original function is defined, so both sin x and cos x must be nonzero. The result uses radian-based trigonometric derivative formulas.