   Chapter 8.4, Problem 48E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding an Equation of a Tangent Line In Exercises 43–50, find an equation of the tangent line to the graph of the function at the given point. Function Point y = sin   x   cos   x ( 3 π 2 ,   0 )

To determine

To calculate: The equation of the tangent line to the graph of the provided function y=sinxcosx at given point (3π2,0).

Explanation

Given Information:

The provided function is y=sinxcosx at given point (3π2,0).

Formula used:

Sine and Cosine differentiation rule:

ddx[sinu]=cosududxddx[cosu]=sinududx

General power rule of differentiation:

ddx[xn]=nxn1

Product rule of differentiation:

ddx[a(x)b(x)]=a(x)b'(x)+b(x)a'(x)

Write the equation of the tangent line at a given point (x1,y1).

yy1=dydx(x1,y1)(xx1)

Here, dydx(x1,y1) represents slope at point (x1,y1).

Calculation:

Consider the provided function:

y=sinxcosx

Differentiate the above function using Sine and Cosine, and product rules of differentiation.

dydx=ddx[sinxcosx]=sinxddx[cosx]+cosxddx[sinx]=sinx(sinx)+cosxcosx=sin2x+cos2x

The derivative of function y=sinxcosx

dydx=sin2x+cos2x

Substitute, 3π2 for x in above derivative

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