write the equation of the plane passingthrough P with normal vector n in (a) normal form

Sunday, October 1, 2017 Math 2211 Chapter 3.4 - Trigonometric Derivatives • d/dx (sin x) = cos x • d/dx (cos x) = -sin x • d/dx (tan x) = sec x • d/dx (csc x) = -(csc x)(cot x) • d/dx (sec x) = sec x tan x • d/dx (cot x) = -csc x - These need to be memorized - Chain rule • Used when there is a function within a function • Theorem f(g(x)) = g’(x)(f’(g(x)) 2 - To demonstrate chain rule, lets use sin(3x + 5x - 4) - First, recognize both the outside and inside functions The inside function is 3x + 5x - 4 • - Called the inside function because it is inside another function • Outside function is sin u - We use u as a placeholder for the inside function so the outside function is easily identifiable. Therefore, we can make u = 3x + 5x - 4 - With our function divided as sin u and u = 3x + 5x - 4, we can begin to differentiate - Take the derivative of the outside function: • d/dx (sin u) = cos u - Take the derivative of the inside function: 1 Sunday, October 1, 2017 d/dx (3x + 5x - 4) = 3x+5 • - Multiply the derivative of the outside function and the inside function: • (3x + 5)(cos u) - Replace u with the original function • Final answer: (3x + 5)(cos (3x + 5x - 4)) 2