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

When using [EmployeeID] as the unique identifier of the Employee table, [EmployeeID] is an example of which of the following? a. Key attribute b. Foreign key c.
A primary reason for Truman's decision to drop the atomic bombs on Japan was that he ____
solve this sum. ....​
Which shapes have two pairs of parallel sides
the length of a rectagle is 5 in longer than its width. if the perimeter of the rectangle is 58 in, find its length and width
Why every values in maths has an approximation ? ( Example : The value of π,... )
a)0.76×0.004b)0.078÷0.5c)0.834+0.79d)0.0034-0.0078​
what is the difference between 4 hundredths and 8 ten thousandths?
Adverse Childhood Experiences A) Are unavoidable B) Have no impact on biology (although they are unpleasant) C) Have been a primary concern in public health sin
What is the factorization of the trinomial below? x^3 - 12x^2 + 35x A. (x - 7)(x + 5) B. x(x - 7)(x - 5) C. (x^2 - 7)(x + 5) D. x(x - 7)(x + 5)