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In the text we noted that if f(u(v(x))) was a composition of three functions, then its derivative is dfdx=dfdu×dudv×dvdx. Write this rule in “prime” notation.

Short Answer

Expert verified

In prime notation the derivative is:

fuv'(x)=f'(uv)(x)×(uv)'(x)×v'(x)

Step by step solution

01

Step 1. Given information:

The composite function and its derivative are:

f(u(v(x)))

dfdx=dfdu×dudv×dvdx

02

Step 2. Derivative in the prime notation:

The derivative of the given composite function is written as:

fuv'(x)=f'(uv)(x)×(uv)'(x)×v'(x)

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