Math Problem Statement

F(x)= 8sec²xtan³x + 16sec⁴xtanx, then f'(x)=?

Solution

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Differentiation
Product Rule
Chain Rule

Formulas

Derivative of sec(x): d/dx[sec(x)] = sec(x)tan(x)
Derivative of tan(x): d/dx[tan(x)] = sec²(x)
Product Rule: d/dx[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)
Chain Rule: d/dx[f(g(x))] = f'(g(x))g'(x)

Theorems

Product Rule
Chain Rule

Suitable Grade Level

Grades 11-12