Let f(æ) = - 6 sin(x)cos(x).dfdad² fda?||

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Answered: Let f(æ) = - 6 sin(x)cos(x). %3D df dx…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Systems Of Linear Equations

Section1.3: Applications Of Systems Of Linear Equations

Problem 13E: Use sin0=0, sin2=1, and sin=0 to estimate sin3.

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Question

Let f(æ) = - 6 sin(x)cos(x).
df
da
d² f
da?
||

Expert Solution

Step 1

Using product rule,

(uv)'= u'v + v'u

Here we take,

u = sinx

v = cosx

df/dx =(uv)' =-6{d(sinx)/dx}*cosx - 6{d(cosx)/dx}*sinx

= cosx*cosx + (-sinx)*sinx

df/dx = -6(cos²x - sin²x)

We know the trigonometric identity that,

cos²x-sin²x = cos2x

Therefore,

df/dx = -6cos2x.

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