differentiate. y = 4x^3 - 5x^2 + 8x + 4 dy/dx = □

Explanation:

Step1: Apply power - rule to each term

The power - rule for differentiation is $\frac{d}{dx}(ax^n)=nax^{n - 1}$. For the term $4x^3$, $\frac{d}{dx}(4x^3)=3\times4x^{3 - 1}=12x^2$. For the term $-5x^2$, $\frac{d}{dx}(-5x^2)=2\times(-5)x^{2 - 1}=-10x$. For the term $8x$, $\frac{d}{dx}(8x)=1\times8x^{1 - 1}=8$. For the constant term $4$, $\frac{d}{dx}(4)=0$.

Step2: Combine the derivatives of each term

$y'=\frac{dy}{dx}=12x^2-10x + 8+0$.

Answer:

$12x^2-10x + 8$