In other words, your final answer should not have any y′ terms in it. When finding the second derivative y′′, remember to replace any y′ terms in your final answer with the equation for y′ you already found. ( ) ( ) ( ) ( ) ( )f x g x f x g x ( ) 1n nd x nxdx, n is any number. When taking the derivative of any term that has a “y” in it multiply the term by y′ (or dy/dx) Download Derivative and Integral Cheat Sheet and more Calculus Cheat Sheet in PDF only on Docsity Common Derivatives and Integrals Derivatives Basic Properties/Formulas/Rules ( ) ( ) ( )d cf x cf x dx, c is any constant. Differentiate both sides of the equation with respect to “x”Ģ. Use whenever you need to take the derivative of a function that is implicitly defined (not solved for y).Įxamples of implicit functions: ln(y) = x2, x3 + y2 = 5, 6xy = 6x+ 2y2, etc.ġ. Same idea for all other inverse trig functions Same idea for all other trig functionsġ1. These rules are all generalizations of the above rules using the chain rule.ĩ.
In the below, u = f(x) is a function of x.
