Math, asked by itsrudra585, 2 months ago

DIfferentiate the equation (2ax^2+bx)

Answers

Answered by shabeehajabin
0

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.

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