Question #5bad2

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Answer 1 · 2017-05-29T08:26:56

#5cos5x - 7sin7x#

#d/dx sincolor(red)(5x) + coscolor(blue)(7x)#

Use the Chain Rule, differentiate outside, then differentiate inside

#color(red)((f(g))' = f'(g)*g')#

To break it down,

First, differentiate #sin(... )#,

#d/dx sin( ...) = cos (... )#

I am using sin( ... ) to show that we are differentiating the outer part first, and ignore the original #5x# first.

Secondly, differentiate inside the parenthesis.

#d/dx ...color(red)(5x) = 5#

Multiply cos(...) with 5.

The proper working is as such:

#d/dx sin5x = 5* cos 5x#

Apply the same workings to #cos 7x#.

#d/dx cos(...) = -sin(...)#
#d/dx ...7x = 7#

Multiply -sin(...) with 7

Thus, #d/dx cos7x = -7sin7x#

#color(blue)(d/dx (sin5x + cos7x) = 5cos5x - 7 sin7x)#