Math, asked by chandresh126, 1 year ago

Differentiate : X^3 + 3X^2 + X

Answers

Answered by nirman95
5

Answer:

Given: y = x³ + 3x² + x

To find : Differentiation of "y" w.r.t "x"

i.e. dy/dx

Calculation :

y = x³ + 3x² + x

=> dy/dx = d(x³)/dx + 3 d(x²)/dx + d(x)/dx

=> dy/dx = 3x² + (3×2)x +1

=> dy/dx = 3x² + 6x + 1

Now, Another information about Differentiation :

1. It will be read as differential of "y" with respect to "x".

2. It represents the instantaneous change of "y" with change in "x".

3. Average change in "y" w.r.t to "x" is denoted as (∆y/∆x).

Answered by Anonymous
111

\large{\underline{\underline{\mathfrak{\green{\sf{Solution:-}}}}}}.

\large{\underline{\underline{\mathfrak{\sf{Find\:here:-}}}}}.

\bold{\:Differentiate\:\:(x^3+3x^2+x)}

\large{\underline{\underline{\mathfrak{\sf{Explanation:-}}}}}.

We can write this ,

\leadsto\:Y\:=\:(x^3+3x^2+x)

Differenciate W.R.To X ,

We find here ,

\leadsto\frac{dY}{dX}\:=\frac{dy}{dx}\:(x^3+3x^2+x)...........(1)

We know ,

  • if \:y\:=\:x^n

So, Differentiate w.r. to x will be

  • \frac{dy}{dx}\:=\:n×\:x^{(n-1)}

Now, by (1)

\leadsto\boxed{\frac{dy}{dx}\:=\:(3x^2+6x+1)}

___________________

Similar questions