What is a Derivative?

A derivative is the result of an operation called differentiation. If we differentiate something, a function, the result tells us how much the function changes with respect to a chosen variable. For instance, the derivative of position with respect to time tells us how much position changes as time changes. This is more commonly known as velocity.

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How to differentiate y=2x(x-2)^5 to find dy/dx?


x^2 + y^2 + 10x + 2y - 4xy = 10. Find dy/dx in terms of x and y, fully simplifying your answer.


Why does the chain rule work?


Given f(x) = (x^4 - 1) / (x^4 + 1), use the quotient rule to show that f'(x) = nx^3 / (x^4 + 1)^2 where n is an integer to be determined.