Math Problem Statement

find the indicated derivative dy/dt where y=(sin(t)tan(t^2+1)

Solution

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Math Problem Analysis

Mathematical Concepts

Differentiation
Product Rule
Chain Rule
Trigonometric Functions

Formulas

Product Rule: d/dt[u(t) * v(t)] = u'(t) * v(t) + u(t) * v'(t)
Chain Rule: d/dt[f(g(t))] = f'(g(t)) * g'(t)
Derivative of sin(t): d/dt[sin(t)] = cos(t)
Derivative of tan(x): d/dt[tan(x)] = sec^2(x)

Theorems

Product Rule
Chain Rule

Suitable Grade Level

Grades 11-12 (Calculus)