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Derivatives Resources

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When you have to take the derivative of 2 variables being multiplied, we use the product rule. If we have f(x)g(x), the derivative will be:   (f(x)g(x))' = f(x)g'(x) + g(x)f'(x).   Now, the primes can be a little confusing when you are learning how to apply this for the first time, so lets denote the number 1 to f(x) and the number 2 to g(x), where 1 refers... read more

Lessons

Differentiation - Taking the Derivative Differentiation is the algebraic method of finding the derivative for a function at any point. The derivative is a concept that is at the root of calculus. There are two ways of introducing this concept, the geometrical way (as the slope of a curve), and the physical way (as a rate of change). The slope of a curve translates to the rate of... read more

Lessons

Derivative Proofs Though there are many different ways to prove the rules for finding a derivative, the most common way to set up a proof of these rules is to go back to the limit definition. This way, we can see how the limit definition works for various functions. We must remember that mathematics is a succession. It builds on itself, so many proofs rely on results... read more