Calcular la derivada de:
$z(x)=(2x^2+3)(5x+3)$
Solución
| Se tiene: | ||
| $f(x)=(2x^2+3)$ | ||
| $g(x)=(5x+3)$ | ||
| Derivada de un producto | ||
| $z'(x)=f'(x)\cdot g(x)+f(x)\cdot g'(x)$ | ||
| $z'(x)=(2x^2+3)'\cdot(5x+3)+(2x^2+3)\cdot(5x+3)'$ | ||
| $z'(x)=(4x^1+0)\cdot(5x+3)+(2x^2+3)\cdot(5+0)$ | ||
| $z'(x)=(4x)\cdot(5x+3)+(2x^2+3)\cdot(5)$ | ||
| $z'(x)=20x^2+12x+10x^2+15$ | ||
| $z'(x)=30x^2+12x +15$ | ||
| Respuesta: | ||
| $z(x)=(2x^2+3)(5x+3)$ | ||
| $z'(x)=30x^2+12x +15$ | ||