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Chapter 2: Q. 4 (page 209)

In the text we noted that if f(u(v(x))) was a composition of three functions, then its derivative is dfdx=dfdu脳dudv脳dvdx. Write this rule in 鈥減rime鈥� notation.

Short Answer

Expert verified

In prime notation the derivative is:

f鈭�u鈭�v'(x)=f'(u鈭�v)(x)脳(u鈭�v)'(x)脳v'(x)

Step by step solution

01

Step 1. Given information:

The composite function and its derivative are:

f(u(v(x)))

dfdx=dfdu脳dudv脳dvdx

02

Step 2. Derivative in the prime notation:

The derivative of the given composite function is written as:

f鈭�u鈭�v'(x)=f'(u鈭�v)(x)脳(u鈭�v)'(x)脳v'(x)

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