- #1

RslM

- 8

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## Homework Statement

May I please have help understanding this example problem in my textbook.

I am working on the chain rule for finding derivatives in Calculus. What I am currently having trouble with is factoring. My textbook gives the follwing example:

f'(x) =(3x - 5)

^{4}(7 - x)

^{10}

f'(x) = (3x - 5)

^{4}x 10(7 - x)

^{9}(-1) + (7 - x)

^{10}4(3x - 5)

^{3}(3)

= -10(3x - 5)

^{4}(7 - x)

^{9}+ (7 - x)

^{10}12(3x - 5)

^{3}

Here it says 2(3x - 5)

^{3}(7 - x)

^{9}is factored out.

= 2(3x - 5)

^{3}(7 - x)

^{9}[-5(3x - 5) + 6(7 - x)]

=2(3x - 5)

^{3}(7 - x)

^{9}(-15x + 25 + 42 - 6x)

And it continues onto simplification.

The area I have trouble with is when 2(3x - 5)

^{3}(7 - x)

^{9}is factored out.

I am not fully understanding why

= 2(3x - 5)

^{3}(7 - x)

^{9}[-5(3x - 5) + 6(7 - x)]

is the result. How was it derived?

Thank you