Question

Trouvez la différentielle de la fonction y=x3⋅sinx

Answer 1

Answer:

The answer is "$y'= x^2( x \cos x + 3 \sin x)$"

Step-by-step explanation:

Given:

$\to y= x^3 \cdot \sin x$

Formula:

$\to \frac{d}{dx} (a b) = a \frac{db}{dx}+b \frac{da}{dx}$

$\to \frac{d}{dx} x^n = nx^{n-1}\\\\\to \frac{d}{dx} \sin x = \cos x$

Differentiate the given value:

$\to y= x^3 \cdot \sin x\\\\ \to y' = x^3 \frac{d}{dx} (\sin x) + \sin x \frac{d}{dx} (x^3)\\\\ \to y'= x^3 \cos x + \sin x \cdot 3x^2\\\\\to y'= x^2( x \cos x + 3 \sin x)$