graciewarren1498 graciewarren1498

03-10-2017
Mathematics

contestada

If f(x) = f(x)g(x), where f and g have derivatives of all orders, show that f'' = f ''g + 2f 'g' + fg''.

Respuesta :

LammettHash LammettHash

03-10-2017

Differentiating once, we have

[tex]f'(x)=f'(x)g(x)+f(x)g'(x)[/tex]

Differentiating again,

[tex]f''(x)=f''(x)g(x)+f'(x)g'(x)+f'(x)g'(x)+f(x)g''(x)[/tex]
[tex]f''(x)=f''(x)g(x)+2f'(x)g'(x)+f(x)g''(x)[/tex]

as needed.

Answer Link

Otras preguntas

how did native American people in different environments get their food?

If you needed information from someone, what type of sentence would you most likely use?

Which responsibilities were assigned to the federal government under the Articles of Confederation? a.taxing goods and services b.maintaining a militia c.drawi

Which of these types of rock can melt under the right conditions?

what is an inequalite

what is a hotel boy in a hotel

Which of the following terms correctly describe the object below. Check all that apply a. pyramid b. polygon c. square d. solid e. polyhedron f. prism

"In the diagram, m = 128° and m = 76°. What is mABC? A) 104 B) 116 C) 128 D) 102 E) 96"

a young boy has been found, and police are trying to locate his family. they take a dna sample from him and begin collecting dna samples from families who have

Indicate the method you would use to prove the two triangles' congruent . If no method applies, enter \"none\". A) SSS. B) SAS. C) ASA. D) AAS. E) NONE