   Chapter 2.3, Problem 51E

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# Find an equation of the tangent line to the curve at the given point. y = 2 x x + 1 , ( 1 , 1 )

To determine

To find: An equation of tangent line to the curve y=2xx+1 at (1, 1)

Explanation

1) Concept:

Differentiate the given function to find the slope and then use it to find equation of line.

2) Formula:

i. Quotient rule: ddxfxgx=gxddxfx-fxddx(gx)gx2

ii. Power rule:  ddxxn=nxn-1

iii. Sum rule: ddxfx+gx=ddxfx+ddxg(x)

iv. Constant multiple rule: ddxCfx=Cddxfx,  where C is constant

v. Constant function rule: ddxC=0, where C is constant

vi. Slope point formula:  y-y1=m  x- x1

3) Given:

y=2xx+1

4) Calculations:

We have y=2xx+1

Differentiate y with respect to x,

By using quotient rule,

y'=x+1ddx2x-2xddx(x+

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