# 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 41E
To determine

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

Expert Solution

The equation of the tangent line is y=20x+1 .

### Explanation of Solution

Given:

The given curve is y=(1+2x)10 and the given point is (0,1) .

Calculation:

Find the slope of the tangent line at the given point (0,1) .

Find first derivative of the given equation y=(1+2x)10 .

Apply chain rule.

Let f=a10,a=1+2x

y'=dda(a10)ddx(1+2x)

Use derivative rule ddx(xn)=nxn1 .

y'=10a9(0+2)y'=20a9

Substitute the value of a=1+2x .

y'=20(1+2x)9

Plug in the x=0 and y=1 into the derivative.

y'=20(1+20)9=20

Slope of the tangent line is 20 .

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

yy1=m(xx1)y1=1,x1=0,m=20y1=20(x0)y1=20xy1+1=20x+1y=20x+1

Hence theequation of the tangent line is y=20x+1 .

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