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Chapter 2: Q. 3 (page 209)

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

(a) in 鈥減rime鈥� notation and

(b) in Leibniz notation.

Short Answer

Expert verified

a) In prime notation the derivative is g鈭�h'(x)=g'(h(x))脳h'(x)

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

(g鈭�h)'(x)=g'(h(x))脳h'(x)

03

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

In Leibniz notation, the derivative is:

dgdx=dgdh脳dhdx

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Most popular questions from this chapter

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.The line tangent to the graph of y=1-x-x2at the point(1,-1)

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