Question

Find the derivative of H when
H(x)= (f(x))^2- (g(x))^2
And
f′(x) = 5g(x), g′(x) = 2f(x).

A)H'(x)=3(f (x) g(x)
B)H'(x)=6(f (x) g(x)
C)H'(x)=7(f (x) + g(x)
D)H'(x)=7f(x) g(x)
E)H'(x)=3(f(x)+g(x))
F)H'(x)=14f(x)g(x)

Answer 1

Use chain rule,
\[(H(x))'=(f(x)^2)'-(g(x)^2)'=2f(x)f'(x)-2g(x)g'(x)\]
Now,
\[f'(x)=5g(x)\\
g'(x)=2f(x)\]
You only have to substitute.

Answer 2

use the chain rule and sub in at the end.

Answer 3

Do you understand it?

Answer 4

After substitute, you'll find,
\[H'(x)=6f(x)g(x)\]

Answer 5

I knew you had to use the chain rule but some times it confuses me lol thank you! @John_ES