Question

if y=(x-3)/(2-5x), then dy/dx=

Answer 1

quotient rule \(f'={\frac {u'v-uv'}{v^{2}}}\)


here \( y'=\dfrac{(x-3)'(2-5x) - (x-3)(2-5x)'}{?????}\)

Answer 2

There is no simpler quest then this :)

Answer 3

I will do a similar example:

Suppose you have the following function, the
derivative (dy/dx) of which you are to find:

\(\color{#000000 }{ \displaystyle y=\frac{2x+5}{3x-8} }\)

The Quotient Rule says: ((f and g , denote functions of x))

\(\color{#000000 }{ \displaystyle \frac{dy}{dx}\left[\frac{f}{g}\right]=\frac{f'g-fg'}{g^2} }\)

The derivative of 2x+5 is 2,
The derivative of 3x-8 is 3.

So,
f'=2 f=2x+5
g'=3 g=3x-8

So let's apply the quotient rule:

\(\color{#000000 }{ \displaystyle \frac{dy}{dx}=\frac{f'g-fg'}{g^2} =\frac{(2)(3x-8)-(2x+5)(3)}{(3x-8)^2} }\)

\(\color{#000000 }{ \displaystyle \frac{dy}{dx}=\frac{6x-16-(6x+15)}{(3x-8)^2} }\)

\(\color{#000000 }{ \displaystyle \frac{dy}{dx}=\frac{-31}{(3x-8)^2} }\)

Answer 4

So I got -13/(2-5x)^2

Answer 5

Fabulous!
That is exactly right!!