The derivative of the function is f'(x) = 9x² tan x⁴ + 4x³(3x³ + 2) sec² x⁴.
<h3>What is the derivative of a function?</h3>
When a single-variable function exists at a given input value, its derivative is represented by the slope of the tangent line to the function's graph at that point.
The given function is f(x) =tan x⁴ · (3x³ + 2).
Differentiate the function with respect to x:
f'(x) = tan x⁴ · 9x² + (3x³ + 2) sec² x⁴· 4x³
= 9x² tan x⁴ + 4x³(3x³ + 2) sec² x⁴
Hence, the derivative of the function is
f'(x) = 9x² tan x⁴ + 4x³(3x³ + 2) sec² x⁴
Learn more about the derivatives:
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