# Find the equation of the tangent line for the given curve.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 3.4, Problem 43E
To determine

## Find the equation of the tangent line for the given curve.

Expert Solution

The equation of the tangent line is y=x+π .

### Explanation of Solution

Given:

The given curve is y=sin(sinx) and the given point is (π,0) .

Calculation:

Find the slope of the tangent line at the given point (π,0) .

Find first derivative of the given equation y=sin(sinx) .

Apply chain rule.

Let f=sina,a=sinx

y'=dda(sina)ddx(sinx)

Use derivative rule ddx(sinx)=cosx .

y'=cosacosx

Substitute the value of a=sinx .

y'=cos(sinx)sinx

Plug in the x=π into the derivative.

y'=cos(sin(π))sin(π)=cos(0)(1)=1(1)=1

Slope of the tangent line is 1 .

Use point-slope form of the equation (For the equation of tangent line).

yy1=m(xx1)y1=0,x1=π,m=1y0=1(xπ)y=x+π

Hence theequation of the tangent line is y=x+π .

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