Question

Find derivative of y(x^2+1)(x^3+3)
using product Rule.
3.​

Answer 1

Answer:

$\boxed{\red{\sf ^{\! dy}/_{\! dx} = 5x^4+3x^2+6x}}$

Step-by-step explanation:

A function is given to us and we need to differentiate it with respect to x Using the Product Rule. The given function is ,

$\sf\dashrightarrow y = (x^2+1)(x^3+3)$

And the Product Rule of Differenciation is ,

• Say if we have two functions u and v and of we need to find the derivative of uv , then it Will be ,

$\sf\dashrightarrow\red{\dfrac{d}{dx}(uv)= u\dfrac{dv}{dx}+v\dfrac{du}{dx}}$

• Now here , let us take , u = x² + 1 and v = x³+3 . So that ,

$\sf\dashrightarrow y = (x^2+1)(x^3+3)$

$\sf\dashrightarrow \dfrac{dy}{dx} = \dfrac{d}{dx}(x^2+1)(x^3+3) \\\\\sf\dashrightarrow \dfrac{dy}{dx}= (x^2+1)\dfrac{d(x^3+3)}{dx}+(x^3+3)\dfrac{d(x^2+1)}{dx} \\\\\sf\dashrightarrow \dfrac{dy}{dx}= (x^2+1)(3x^2) + (x^3+3)(2x) \\\\\sf\dashrightarrow \dfrac{dy}{dx}= 3x^4+3x^2+2x^4+6x \\\\\sf\dashrightarrow \underset{\blue{\sf Required\ Derivative}}{\underbrace{\boxed{\pink{\sf \dfrac{dy}{dx}= 5x^4+3x^2+6x}}}}$

Hence the required derivative of the function is 5x⁴ + 3x² + 6x .