Question

DIfferentiate the equation (2ax^2+bx)

Answer 1

Answer:

$4ax+b$ is the differential for the equation $2ax^{2} +bx$

Step-by-step explanation:

The question is to differentiate the equation $2ax^{2} +bx$.

Consider $y=2ax^{2} +bx$. We want to find $\frac{dy}{dx}$. We will solve this equation using the chain rule.

       Let  $u=2ax^{2}$ and $v=bx$ , then  $\dfrac{dy}{dx}=\frac{d}{dx}( u+v)$  → (1)

Where 'u' and 'v' are the differential function of 'x',

          ∴    $\frac{du}{dx}=2a2x=4ax$  

              $\dfrac{dv}{dx}=b$

Here we used the formula $\frac{d\left(x^n\right)}{dx}=nx^{n-1};\frac{d\left(x^2\right)}{dx}=2^{x^2-1}=2x$ and $\frac{d\left(x\right)}{dx}=1;\frac{d\left(bx\right)}{dx}=b\frac{dx}{dx}=b$

Now substitute the values of $\frac{du}{dx}$ and $\frac{dv}{dx}$ in equation (1). Then we will get as follows,

      $\dfrac{dy}{dx}=4ax+b$

This is the answer for the question.