Calculate the derivatives (f(g(x)))' and (g(f(x))' if f(x) = x³ 1 g(x) : бх + 1 (Express numbers in exact form. Use symbolic notation and fractions where needed.) (F(g(x))' = (g(f(x)))' =

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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### Calculating Derivatives of Composed Functions

In this example, we will calculate the derivatives \( (f(g(x)))' \) and \( (g(f(x)))' \) for the given functions:

\[ f(x) = x^5 \]

\[ g(x) = \frac{1}{6x + 1} \]

(Express numbers in exact form. Use symbolic notation and fractions where needed.)

#### Derivative Computations:

1. \( (f(g(x)))' = \)

2. \( (g(f(x)))' = \)
Transcribed Image Text:### Calculating Derivatives of Composed Functions In this example, we will calculate the derivatives \( (f(g(x)))' \) and \( (g(f(x)))' \) for the given functions: \[ f(x) = x^5 \] \[ g(x) = \frac{1}{6x + 1} \] (Express numbers in exact form. Use symbolic notation and fractions where needed.) #### Derivative Computations: 1. \( (f(g(x)))' = \) 2. \( (g(f(x)))' = \)
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