If {eq}f(x) = 6x^2 - 12x - 40 {/eq}, find {eq}{f}'(x) {/eq} and {eq}{f}'(-1) {/eq}.


If {eq}f(x) = 6x^2 - 12x - 40 {/eq}, find {eq}{f}'(x) {/eq} and {eq}{f}'(-1) {/eq}.

Difference Rule:

According to the difference rule, for a given function, {eq}s(x)=f(x)-g(x) {/eq}, the derivative {eq}s'(x) {/eq} is given by:

{eq}\begin{align} \frac{d}{dx}s(x)&=\frac{d}{dx}(f(x)-g(x))\\ &=\frac{d}{dx}f(x) - \frac{d}{dx}g(x)\\ \implies s'(x)&=f'(x)-g'(x) \end{align} {/eq}.

Answer and Explanation:

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We are given: A function, {eq}f(x) = 6x^2 - 12x - 40 {/eq}.

We are asked to determine {eq}{f}'(x) {/eq}, {eq}{f}'(1) {/eq}, and...

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How to Compute Derivatives


Chapter 20 / Lesson 1

Understand what derivative calculus is and how to find the derivative of a function. Learn the derivative rules, and practice taking derivatives by following examples.

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