3.3 Derivatives- Power Rule, Product & Quotient

The Power Rule states that if $$y = x^n$$ , then the derivative $$y' = nx^{n-1}$$ .

The Product Rule states that if $$y = u \times v$$ , then the derivative $$y' = u'v + uv'$$ , where $$u'$$ and $$v'$$ are the derivatives of $$u$$ and $$v$$ respectively.

The Quotient Rule states that if $$y = \frac{u}{v}$$ , then the derivative $$y' = \frac{u'v - uv'}{v^2}$$ .

$$y' = -\frac{5}{(x-3)^2}$$ .

$$y' = x^2 e^x (x + 3)$$ .

Yes, differentiating a function refers to the process of finding its derivative.

The slope is $$2$$ .

$$\frac{dy}{dx} = -\frac{6x}{(4+x^2)^2}$$ .

The derivative represents the slope of the tangent line to the graph of the function at a given point.

A derivative of zero indicates a potential maximum, minimum, or inflection point on the graph.