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Consider f : R and g: R- differentiable functions. Suppose that D (g(x)) is a matrix whose rows are R1, Ro and Rz and Df(2) is a matrix whose column are C1 and C2. Then the entry corresponding to the 1st row and 1st column of the derivative of h(x) = g(f(x)) is (The · can be seen as a product of matrices or as the dot product of the appropriate vectors ) R1 · C1 R1 · (C1 + C2) (R1 + R2) · C1 (R1 + R2) · (C1 + C2)

Consider f : R and g: R- differentiable functions. Suppose that D (g(x)) is a matrix whose rows are R1, Ro and Rz and Df(2) is a matrix whose column are C1 and C2. Then the entry corresponding to the 1st row and 1st column of the derivative of h(x) = g(f(x)) is (The · can be seen as a product of matrices or as the dot product of the appropriate vectors ) R1 · C1 R1 · (C1 + C2) (R1 + R2) · C1 (R1 + R2) · (C1 + C2)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider \( f: \mathbb{R}^2 \to \mathbb{R}^3 \) and \( g: \mathbb{R}^3 \to \mathbb{R}^2 \), differentiable functions. Suppose that \( D_g(f(x)) \) is a matrix whose rows are \( R_1, R_2, \) and \( R_3 \) and \( D_f(x) \) is a matrix whose column are \( C_1 \) and \( C_2 \). Then the entry corresponding to the 1st row and 1st column of the derivative of \( h(x) = g(f(x)) \) is *(The \(\cdot\) can be seen as a product of matrices or as the dot product of the appropriate vectors)* - \( R_1 \cdot C_1 \) - \( R_1 \cdot (C_1 + C_2) \) - \((R_1 + R_2) \cdot C_1\) - \((R_1 + R_2) \cdot (C_1 + C_2)\) The correct option is: - \((R_1 + R_2) \cdot C_1\)
Transcribed Image Text:Consider \( f: \mathbb{R}^2 \to \mathbb{R}^3 \) and \( g: \mathbb{R}^3 \to \mathbb{R}^2 \), differentiable functions. Suppose that \( D_g(f(x)) \) is a matrix whose rows are \( R_1, R_2, \) and \( R_3 \) and \( D_f(x) \) is a matrix whose column are \( C_1 \) and \( C_2 \). Then the entry corresponding to the 1st row and 1st column of the derivative of \( h(x) = g(f(x)) \) is *(The \(\cdot\) can be seen as a product of matrices or as the dot product of the appropriate vectors)* - \( R_1 \cdot C_1 \) - \( R_1 \cdot (C_1 + C_2) \) - \((R_1 + R_2) \cdot C_1\) - \((R_1 + R_2) \cdot (C_1 + C_2)\) The correct option is: - \((R_1 + R_2) \cdot C_1\)
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