J5keAvilarklindygla
J5keAvilarklindygla J5keAvilarklindygla
  • 04-08-2016
  • Mathematics
contestada

Solve the equation below:
Let f and g be differentiable functions such that
f(1) = 4, g(1) = 3, f'(3) = -5, f'(1) = -4, g'(1) = -3, g'(3) = 2
If H(x) = f(g(x)), then h'(1) =

Respuesta :

Hagrid
Hagrid Hagrid
  • 08-08-2016
Remember the chain rule.
L(x)=f(g(x))

L'(x)=f'(g(x))g'(x)

take the derivative of f(g(x)). just treat them like they are variables. so you get:

h'=f'(g(x))g'(x)

now plug in your x value and evaluate:

h'(1)=f'(g(1))(g'(1))


substitute in values that you know and evaluate again
h'(1)=f'(3)(-3)

h'(1)=(-5)(-3)=15

Answer Link

Otras preguntas

In the library there are 200 books. 58 of them are non-fiction. What percentage of the books are non-fiction?
how do I solve this proportion?
a piece of wood is 180cm long, Tom cuts it into three pieces in the ratio 2:3:4 Work out the length of the longest piece
What is the electron configuration of helium
Put brackets in the expression below so that it's value is 45.024. 1.6 + 3.8 * 2.4 *4.2 (*= times )
If the function h(x) represents the number of full hours that it takes a person to assemble x sets of tires in a factory, which would be an appropriate domain f
List two factors that might cause an organism to restrict its use of a resource.
How is carbon dioxide obtained?
The sum of a number and 18 times its reciprocal is 11. Find the number(s). Let x represent the unknown number. The Reciprocal of x is____?
find the difference: 7 7/8 - 3 1/4