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

What language do the Persians in Iran speak? Arabic French Farsi Hindu

Which definition is the best for “semipermeable membrane”?

Determine whether each of the following topics would more likely be studied in microeconomics or macroeconomics. Microeconomics Macroeconomics The effect of fed

Which executive department is the largest? the Department of Labor the Department of Justice the Department of Homeland Security the Department of De

An airplane traveling at half the speed of sound emits a sound of frequency 4.68 kHz. (a) At what frequency does a stationary listener hear the sound as the pla

Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (1, 0, 9) and perpendicular to the plane x + 2y

What is the following product? 3sqrt4 * sqrt3

Where is the cell is the glucose produced

4. Why do you think countries that formerly possessed nuclear weapons, such as Ukraine and SouthAfrica, may have given them up? Why do you think other countries

A pedestal for a statue is in the shape of a hexagon, formed by a square and two congruent triangles, with the dimensions shown below. What is the area of the t