LIFESCI 30A Lecture Notes - Lecture 14: Quotient Rule, Product Rule, Power Rule

• School: UCLA
• Department: Life Sciences
• Course: LIFESCI 30A
• Professor: Conley William Joseph

Document Summary

Rules for computing the derivative of a function, given a formula for it: (f(x) = ___) D/dx (xn) = n*xn-1 ***if n is any constant ( power rule ) D/dx( f(x) + g(x) ) = d/dx( f(x) ) + d/dx( g(x) ) or (f+g)" = f" + g". D/dx( f(x) - g(x) ) = d/dx( f(x) ) - d/dx( g(x) ) or (f-g)" = f" g". D/dx(f(x)*g(x)) = d/dx(f(x))*g(x) + f(x)* d/dx(g(x)) or (f*g)" = (f")*g + f*(g") Examples: d/dx(x2*x3) = d/dx(x2)*x3 + (x2)* d/dx(x3) 2x*x3 + x2*3x2 2x4 + 3x4 = 5x4. Low dhigh less high dlow with the low squared below. D/dx(f(x) / g(x)) = [g(x)*f"(x) f(x)*g"(x)] / (g(x))2 or (g*f" f*g") / g2. D/dx(f(g(x))) = (f o g)" = f"(g(x))*g"(x) D/dx(c*f(x)) = c d/dx(f(x)) or (cf)" = c*f" if c is a constant. D/dx(f(x) + c) = d/dx(f(x)) or (f + constant) = f" for any constant. Suppose we know f"(t) and we want to know f(t).