Math Problem Statement

Find the derivative. y equals 2 left parenthesis 5 Superscript StartRoot x EndRoot Baseline right parenthesis Question content area bottom Part 1 A.StartFraction dy Over dx EndFraction equals ln 5 left parenthesis 5 Superscript StartRoot x EndRoot Baseline right parenthesis left parenthesis StartRoot x EndRoot right parenthesis StartFraction dy Over dx EndFraction equals ln 5 left parenthesis 5 Superscript StartRoot x EndRoot Baseline right parenthesis left parenthesis StartRoot x EndRoot right parenthesis B.StartFraction dy Over dx EndFraction equals StartFraction ln 5 left parenthesis 5 Superscript StartRoot x EndRoot Baseline right parenthesis Over StartRoot x EndRoot EndFraction StartFraction dy Over dx EndFraction equals StartFraction ln 5 left parenthesis 5 Superscript StartRoot x EndRoot Baseline right parenthesis Over StartRoot x EndRoot EndFraction C.StartFraction dy Over dx EndFraction equals 2 ln 5 left parenthesis 5 Superscript StartRoot x EndRoot Baseline right parenthesis left parenthesis StartRoot x EndRoot right parenthesis StartFraction dy Over dx EndFraction equals 2 ln 5 left parenthesis 5 Superscript StartRoot x EndRoot Baseline right parenthesis left parenthesis StartRoot x EndRoot right parenthesis D.StartFraction dy Over dx EndFraction equals StartFraction 2 ln 5 left parenthesis 5 Superscript x Baseline right parenthesis Over StartRoot x EndRoot EndFraction StartFraction dy Over dx EndFraction equals StartFraction 2 ln 5 left parenthesis 5 Superscript x Baseline right parenthesis Over StartRoot x EndRoot EndFraction

Solution

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Math Problem Analysis

Mathematical Concepts

Differentiation
Exponential Functions
Chain Rule

Formulas

Derivative of exponential functions: d/dx [a^u(x)] = a^u(x) * ln(a) * d/dx(u(x))
Chain Rule: d/dx[f(g(x))] = f'(g(x)) * g'(x)
Derivative of square root: d/dx[√x] = 1/(2√x)

Theorems

Chain Rule
Exponential Function Differentiation Theorem

Suitable Grade Level

Grades 11-12, College Level Calculus

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