Differentiation Rules

# Differentiation Rules - x and v(x ≠ 0 then the quotient...

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Differentiation Rules Definition The derivative of the function f with respect to the variable x is the function f’ whose value at x is F’(x) = Lim h x f h x f h ) ( ) ( 0 - + Rule 1: Derivative of a Constant If c is the constant, then d/dx c = 0 Rule 2: Power Rule for Positive Integers If n is a positive integer, then d/dx x n = nx n-1 Rule 3: The Constant Multiple Rule If u is a differentiable function of x , and c is a constant, then d/dx(cu) = c du/dx Rule 4: The Sum Rule If u and v are differentiable functions of x , then their sum u + v is differentiable at every point where u and v are both differentiable. At such points, d/dx (u+v) = du/dx + dv/dx Rule 5: The Product Rule If u and v are differentiable at x , then so is their product uv , and d/dx(uv) = u dv/dx + v du/dx Rule 6: The Quotient Rule If u and v are differentiable at

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Unformatted text preview: x , and v(x) ≠ 0, then the quotient u/v is differentiable at x , and 2 v dx dv u dx du v v u dx d-= Rule 7: Power Rule for Negative Integers If n is a negative integer and x ≠ 0, then d/dx (x n ) = nx n-1 Rule 8: Power Chain Rule d/dx u n = nu n-1 du/dx Implicit Differentiation Steps: 1. Differentiate both sides of the equation with respect to x , treating y as a differentiable function of x . 2. Collect the terms with dy/dx on the side of the equation. 3. Factor out dy/dx. 4. Solve for dy/dx by dividing. Derivatives of Trigonometric Functions d/dx ( sin x) = co s x d/dx ( cos x) = -sin x d/dx (tan x) = sec 2 x d/dx (sec x) = sec x tan x d/dx( cot x) = -csc 2 x d/dx ( csc x) = -csc x cot x...
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Differentiation Rules - x and v(x ≠ 0 then the quotient...

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