Question

f(x)=2x⁷+8x¹¹+2x⁶-9x²+13
Assinale a alternativa que corresponde a sua derivada

Answer 1

Resposta:

14X^6+88X^10+12X^5-18X+C

Explicação passo a passo:

Answer 2

Resposta:

$\sf f(x)=2x^7+8x^{11}+2x^6-9x^2+13$

$\sf f'(x)=\frac{d}{dx}(2x^7+8x^{11}+2x^6-9x^2+13)$

$\sf f'(x)=\frac{d}{dx}2x^7+\frac{d}{dx}8x^{11}+\frac{d}{dx}2x^6-\frac{d}{dx}9x^2+\frac{d}{dx}13$

$\sf f'(x)=2\cdot\frac{d}{dx}x^7+8\cdot\frac{d}{dx}x^{11}+2\cdot\frac{d}{dx}x^6-9\cdot\frac{d}{dx}x^2+0$

$\sf f'(x)=2\cdot7\cdot x^{7-1}+8\cdot11\cdot x^{11-1}+2\cdot6\cdot x^{6-1}-9\cdot2\cdot x^{2-1}$

$\red{\boxed{\sf f'(x)=14x^6+88x^{10}+12x^5-18x}}$

Regras de derivação usadas:

• $\sf \frac{d}{dx}(f(x)\pm g(x))=\frac{d}{dx}f(x)\pm\frac{d}{dx}g(x)$

• $\sf \frac{d}{dx}(a\cdot f(x))=a\cdot\frac{d}{dx}f(x)$

• $\sf\frac{d}{dx} x^n=n\cdot x^{n-1}$

• $\sf\frac{d}{dx}a=0$