Question #014c0

Question

Question #014c0

1 Answer

Impact of this question

1591 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-08T12:30:09

$\frac{d^{2}}{{d x}^{2}} (\frac{3 x + 4}{2 x - 5}) = \frac{92}{{(2 x - 5)}^{3}}$ $d^2/dx^2 ((3x+4)/(2x-5) )= 92 /(2x-5)^3$

Explanation:

Use the quotient rule:

$\frac{d}{d x} \frac{3 x + 4}{2 x - 5} = \frac{(2 x - 5) \frac{d}{d x} (3 x + 4) - (3 x + 4) \frac{d}{d x} (2 x - 5)}{{(2 x - 5)}^{2}}$ $d/dx(3x+4)/(2x-5) = ( ( 2x-5) d/dx (3x+4) - (3x+4)d/dx(2x-5))/(2x-5)^2$

$\frac{d}{d x} \frac{3 x + 4}{2 x - 5} = \frac{3 (2 x - 5) - 2 (3 x + 4)}{{(2 x - 5)}^{2}}$ $d/dx(3x+4)/(2x-5) = ( 3( 2x-5) - 2(3x+4))/(2x-5)^2$

$\frac{d}{d x} \frac{3 x + 4}{2 x - 5} = \frac{6 x - 15 - 6 x - 8}{{(2 x - 5)}^{2}} = - \frac{23}{{(2 x - 5)}^{2}}$ $d/dx(3x+4)/(2x-5) = (6x -15 -6x -8 )/(2x-5)^2 = - 23 /(2x-5)^2$

Now:

$\frac{d^{2}}{{d x}^{2}} \frac{3 x + 4}{2 x - 5} = \frac{d}{d x} (- \frac{23}{{(2 x - 5)}^{2}})$ $d^2/dx^2 (3x+4)/(2x-5) = d/dx (- 23 /(2x-5)^2)$

$\frac{d^{2}}{{d x}^{2}} \frac{3 x + 4}{2 x - 5} = \frac{46}{{(2 x - 5)}^{3}} \frac{d}{d x} (2 x - 5)$ $d^2/dx^2 (3x+4)/(2x-5) = 46 /(2x-5)^3 d/dx (2x-5)$

$\frac{d^{2}}{{d x}^{2}} \frac{3 x + 4}{2 x - 5} = \frac{92}{{(2 x - 5)}^{3}}$ $d^2/dx^2 (3x+4)/(2x-5) = 92 /(2x-5)^3$

Science

Math

Humanities

... and beyond

Question #014c0

1 Answer

Explanation:

Related questions

Impact of this question