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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

47–48 Find an equation of the tangent to the curve at the given point.

y = 4 sin 2 x , ( π / 6 , 1 )

To determine

To find: Equation of tangent to the curve.

Explanation

1) Formula:

i. Constant multiplication rule:

ddxk.fx=k.ddxf(x)

ii. Chain rule: Let Fx=fgx, if g is differentiable at x and f is differentiable at g(x) then F'x=f'gxg'(x)

iii.

ddxsinx=cosx

iv. Equation of tangent line to the curve y=f(x) at point (a,f(a)) is, (y-f(a))=f(a)(x-a)

2) Given:

y=4 sin2x,      (π/6 ,1)

3) Calculation:

Differentiate y with respect to x,

f'(x)=ddx4 sin2x

By using constant multiplication and chain rule,

ddx4 sin2x=4.ddxsin2x=4.2sinx.ddxsinx=8sinx

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