Math Problem Statement

y=xsin x^{\sin\text{ x}},d2y/dx2

Solution

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Math Problem Analysis

Mathematical Concepts

Implicit Differentiation
Logarithmic Differentiation
Product Rule
Chain Rule

Formulas

y = x^{\sin(x)}
\ln(y) = \sin(x) \ln(x)
First derivative: \frac{dy}{dx} = x^{\sin(x)} \left( \cos(x) \ln(x) + \frac{\sin(x)}{x} \right)
Second derivative: \frac{d^2y}{dx^2} = \frac{d}{dx} \left[ x^{\sin(x)} \left( \cos(x) \ln(x) + \frac{\sin(x)}{x} \right) \right]

Theorems

Product Rule
Chain Rule
Logarithmic Differentiation

Suitable Grade Level

University Level (Calculus)