Question
Asked Apr 11, 2019
58 views

Suppose that f : R → R is differentiable and define g(x) = x^3 f(x^3). Show that g is differentiable and compute g′

check_circle

Expert Answer

Step 1

Given:

The function f : R → R is differentiable.

The function g(x) = x3 f(x3).

Step 2

Proof:

It is known that  x3  is differentiable, then by the given it can be stated that f(x3) is also differenitable.

Now show that x3 f(x3) is differentiable.

The prduct of two differentiable function is said to be differentiable. That is, if  h(x) and s(x) are two differentiable functions, then h(x)s(x) is also differentiable.

Thus, it can be concluded that g =  x3 f(x3) is differentiable.

 

Step 3

Calculation:

Differentiate the given g(x) with resp...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Advanced Math

Related Advanced Math Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Find the point of intersection of the given pair of straight lines x - 4y = -2 x + 2y =4

A: Simplify the equation x-4y=-2 as follows.

question_answer

Q: 3. Suppose f(z) is continuous in the closed disk {려くR) and analytic in the open disk {|z| < R). Show...

A: To extend Cauchy's theorem to the boundary of the domain of anaylyticity ,under the given conditions

question_answer

Q: Abstract Algebra

A: To prove that mulitplication and division can be performed by striaghtedge and compass constructions

question_answer

Q: Draw the Venn diagram: The 3 most common colors in the 193 flags of the member nations of the UN ar...

A: To represent the given data about the three sets (R, W and B denoting the colours red , white and bl...

question_answer

Q: Given the differential equation: xy"+y'+xy=0, x0=1 Find: Seek the power series solutions to the giv...

A: Consider the differential equation

question_answer

Q: Abstract Algebra Proofs: Looking for assistance on this problem, please.

A: Let G be an abelian group, and H be a subgroup of G.To prove: H is a normal subgroup.Proof: We have ...

question_answer

Q: Write 2x^2-3x+7= x^3+the square root of x-1  as it might have appeared in each of the following sour...

A: To represent the given equation as notated by the various mathematicians (belonging to different tim...

question_answer

Q: This exercise considers a crystal whose unit cell has base vectors that are not necessarily mutually...

A: To discuss the properties of the reciprocal basis to the given basis of vectors

question_answer

Q: Give an example of a random variable and an example of a non-random variable.

A: Random variables: -Different type of processes which are random in nature result into the numbers an...