Question

y=2x+3/4x+5 find dy/dx​

Answer 1

Step-by-step explanation:

$y = 2x + \frac{3}{4} x + 5 \\ \frac{dy}{dx} = 2 + \frac{3}{4} = \frac{8 + 3}{4} \\ \frac{dy}{dx} = \frac{11}{3}$

Answer 2

$y = \dfrac{2x + 3}{4x + 5} \\ \\ \dfrac{dy}{dx} = \dfrac{ \dfrac{d(2x + 3)}{dx}(4x + 5) - \dfrac{d(4x + 5)}{dx}(2x + 5)}{(4x + 5)^{2}} \\ \\ \dfrac{dy}{dx} = \frac{2(4x + 5) - 4(2x + 3)}{(4x + 5)^{2} } \\ \\ \dfrac{dy}{dx} = \frac{(8x + 10) - (8x + 12)}{(4x + 5)^{2} } \\ \\ \dfrac{dy}{dx} = \frac{10- 12}{(4x + 5)^{2} } \\ \\ \dfrac{dy}{dx} = \frac{ - 2}{(4x + 5)^{2} }$

Quick review :

(u/v)' = u'v - uv'/v² (Quotient rule)

Differentiation of constant is 0

Differentiation of x is 1

Some more formulae :

Differentiation of sinx is cosx

Differentiation of cosx is - sinx

(u ± v)' = u' ± v' (Addition and subtraction rule)

(uv)' = u'v + uv' (Product rule)