   Chapter 8.4, Problem 49E ### 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 = ln ( sin   x + 2 ) ( 3 π 2 ,   0 )

To determine

To calculate: The equation of the tangent line to the graph of the provided function y=ln(sinx+2) at given point (3π2,0).

Explanation

Given Information:

The provided function is y=ln(sinx+2) at given point (3π2,0).

Formula used:

Sine differentiation rule:

ddx[sinu]=cosududx

General power rule of differentiation:

ddx[xn]=nxn1

Logarithmic rule of differentiation:

ddx[ln(u)]=1ududx

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=ln(sinx+2)

Differentiate the above function using Sine, logarithmic rules of differentiation.

dydx=ddx[ln(sinx+2)]=1(sinx+2)ddx[sinx+2]=1(sinx+2)(cosx)

The derivative of function y=ln(sinx+2)

dydx=cosxsinx+2

Substitute, 3π2 for x in above derivative

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