Question

Differentiate. y 5 ody (AX (52 O dy 5 (4x - 52

Answer 1

`(dy)/(dx)\text{ = }(-5)/((4x-5)^2)`

Step-by-step explanation

We want to differentiate y given:

`y\text{ = }\frac{x}{4x\text{ - 5}}`

To differentiate fractions as this, we first spllit the numerator and denominator as:

U = x

V = 4x - 5

Now, differentiate them separately.

dU/dx = 1

dV/dx = 4

Now, use formula:

`(dy)/(dx)\text{ =}\frac{V(du)/(dx)\text{ - U}(dV)/(dx)}{V^2}`

So, let us put those values in there:

`\begin{gathered} (dy)/(dx)\text{ = }\frac{(4x\text{ - 5) }\cdot\text{ 1 - (x }\cdot\text{ 4)}}{(4x-5)^2} \\ (dy)/(dx)\text{ = }\frac{4x\text{ - 5 - 4x}}{(4x-5)^2} \\ (dy)/(dx)\text{ = }(-5)/((4x-5)^2) \end{gathered}`

That is the answer