Question

if
y=2x + 3/4x² + 5x +6
find dy/dx​

Answer 1

Answer:

x - 6/4x³ + 5

Step-by-step explanation:

y = 2x + 3/4x² + 5x +6

dy/dx = x - 6/4x³ + 5

Answer 2

Given,

y = 2x + 3/4x² + 5x + 6.

To find,

The derivative that is, dy/dx.

Solution,

We can solve this problem by following the below process.

So, the derivative or differentiation can be defined as the rate of change of a quantity with respect to any other quantity. For example, velocity is a derivative and is the rate of change of distance with respect to time.

Firstly, let's simplify the given expression

y = 2x + 3/4x² + 5x + 6

⇒ y = 7x + 3/4x² + 6.

To find the derivative of the given 'y', we should know some basic rules. Few such important rules are,

$\frac{dy}{dx} (x^n)=nx^{(n-1)}$, and

$\frac{dy}{dx} (Constant)=0$.

Now,

$\frac{dy}{dx}=\frac{d}{dx} (7x)+\frac{d}{dx} (\frac{3}{4x^2})+\frac{d}{dx} (6)$

$\frac{dy}{dx}=7\frac{d}{dx} (x)+\frac{3}{4} \frac{d}{dx} (x^{-2}})+\frac{d}{dx} (6)$

From the above rules,

$\frac{dy}{dx}=7(1x^{1-1})+\frac{3}{4} (-2x^{-2-1})+(0)$

$\frac{dy}{dx}=7(1x^{0})+\frac{3}{4} (-2x^{-3})+(0)$

$\frac{dy}{dx}=7+\frac{3}{4} (\frac{-2}{x^{3}})$

$\frac{dy}{dx}=7-\frac{3}{2} (\frac{1}{x^{3}})$

$\frac{dy}{dx}=7-\frac{3}{2x^{3}}$

Therefore, for y = 2x + 3/4x² + 5x + 6, the dy/dx will be $7-\frac{3}{2x^{3}}$.