menu
bartleby
search
close search
Hit Return to see all results

Use the information about values of the functions and their derivatives to calculate H'(6), where H(x)хf'(6)g' (6)f(6)g(6)9-82-3(Give an exact answer. Use symbolic notation and fractions where needed.)Н (6)

Question
Use the information about values of the functions and their derivatives to calculate H'(6), where H(x)
х
f'(6)
g' (6)
f(6)
g(6)
9
-8
2
-3
(Give an exact answer. Use symbolic notation and fractions where needed.)
Н (6)
help_outline

Image Transcriptionclose

Use the information about values of the functions and their derivatives to calculate H'(6), where H(x) х f'(6) g' (6) f(6) g(6) 9 -8 2 -3 (Give an exact answer. Use symbolic notation and fractions where needed.) Н (6)

fullscreen
check_circleAnswer
Step 1

Given,

х
Н(2)
g(x)f(x)
g (6)
f'(6)
f(6)
g(6)
9
-8
2
-3
help_outline

Image Transcriptionclose

х Н(2) g(x)f(x) g (6) f'(6) f(6) g(6) 9 -8 2 -3

fullscreen
Step 2

Now, differentiating the H(x) with respect to x, we get

аH (x)
Н'(x)
dx
х
g(x)f (x).
dx
g(x)f(x)ddg(x)f(x2))
dx
-x-
(g(x)f (x)2
g(x)f(x)(1)-x(g'(x)f (x)-g(x)f'(x))
(g (x)f(x))2
g(x)f (x)-x(g' (x)f(x)-g(x)f'(x))
(g(x)f(x))2
help_outline

Image Transcriptionclose

аH (x) Н'(x) dx х g(x)f (x). dx g(x)f(x)ddg(x)f(x2)) dx -x- (g(x)f (x)2 g(x)f(x)(1)-x(g'(x)f (x)-g(x)f'(x)) (g (x)f(x))2 g(x)f (x)-x(g' (x)f(x)-g(x)f'(x)) (g(x)f(x))2

fullscreen
Step 3

Now, putting the required values from the ...

g(6)f(6)-6(g'(6)f(6)-g(6)f'(6))
(g(6)f(6)2
:. H'(6) =
2x9-6(-3x9-2(-8))
(2x9)2
18-6(-27+16)
324
18+66
324
27
help_outline

Image Transcriptionclose

g(6)f(6)-6(g'(6)f(6)-g(6)f'(6)) (g(6)f(6)2 :. H'(6) = 2x9-6(-3x9-2(-8)) (2x9)2 18-6(-27+16) 324 18+66 324 27

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Calculus

Derivative

Sorry about that. What wasn’t helpful?