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Chapter 2: Q. 9 (page 197)

Use the product rule to find and state the rule for differentiation of a product of three functions f, g, h in other words(f(x)g(x)h(x))'

Short Answer

Expert verified

The derivative can be given as

(f(x)g(x)h(x))'=(f(x)g(x))h'(x)+f'(x)g(x)h(x)+f(x)g'(x)h(x)

Step by step solution

01

Given information

We are given a product of three functions(f(x)g(x)h(x))'

02

Use product rule to find the derivative

We get,

(f(x)g(x)h(x))'=(f(x)g(x))h'(x)+(f(x)g(x))'h(x)=(f(x)g(x))h'(x)+f'(x)g(x)h(x)+f(x)g'(x)h(x)

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Most popular questions from this chapter

Find the derivative of the absolute value function and piecewise defined function

f(x)=3x+1ifx鈮�1x3ifx>1

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=(x+1)(3x-4)x3-27

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=3x-4(2x+1)6

Use the definition of the derivative to find f' for each function f in Exercises 39-54

f(x)=-x3-x+1

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.
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