Question #5bad2

1 Answer
May 29, 2017

5cos5x - 7sin7x

Explanation:

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)