BuyFind

Single Variable Calculus: Concepts...

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

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

Answer to Problem 43E

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.

  df(a)dx=dfdadadx

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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