   Chapter 3.3, Problem 2E

Chapter
Section
Textbook Problem

Differentiate.f(x) = x cos x + 2 tan x

To determine

To find:  The differentiation of f(x)=xcosx+2tanx.

Explanation

Given:

The function is,f(x)=xcosx+2tanx.

Formula used:

The Product Rule:

The product rule for two functions f1(x) and f2(x) is given as follows.

ddx[f1(x)f2(x)]=f1(x)ddx[f2(x)]+f2(x)ddx[f1(x)] (1)

The Sum Rule:

If g1(x) and g2(x) are function, then the differentiation form is,

ddx[g1(x)+g2(x)]=ddx[g1(x)]+ddx[g2(x)] (2)

The Power Rule:

If n is a real number, then the power rule is,

ddx(xn)=nxn1 (3)

The Constant Multiple Rule:

If c is a constant and f(x) is a function, then the differentiation form is,

ddx[cf(x)]=cddx[f(x)] (4)

Calculation:

In equation (2), substitute xcosx for g1(x) and 2tanx for g2(x).

ddx(xcosx+2tanx)=ddx(xcosx)+ddx(2tanx)       (5)

In equation (1), substitute x for f1(x) and cosx for f2(x)

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