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State the chain rule for differentiating a composition g(h(x))of two functions expressed

(a) in “prime” notation and

(b) in Leibniz notation.

Short Answer

Expert verified

a) In prime notation the derivative is gh'(x)=g'(h(x))×h'(x)

b) In Leibniz notation the derivative is:dgdx=dgdh×dhdx

Step by step solution

01

Step 1. Given information:

The composite function is:

g(h(x))

02

Part (a). Step 1. The derivative in prime notation:

In prime notation the derivative of the function is written as:

(gh)'(x)=g'(h(x))×h'(x)

03

Part (b). Step 1. The derivative in Leibniz notation:

In Leibniz notation, the derivative is:

dgdx=dgdh×dhdx

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