This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Section 3.2: Derivative Rules
Powers, Multiples, Sums, Differences
1. Derivative of a Constant Function If f (x) = c for a constant c then Proof: 2. Power Rule If n is any real number, then for all x where the powers xn , xn1 are defined. 1 Example:
Find the derivatives of f (x) = x, g(x) = x, h(x) = x3 , k(x) = x2+ 3. Constant Multiple Rule If u is a differentiable function of x, and c is a constant, then Examples
Find
d (3x2 ), dx d (u) dx 2 4. Derivative Sum and Difference Rules If u, v are both differentiable functions with respect to x, then at every point where both u and v are differentiable. Example
4 Find y (x) where y = x3 + 3 x2  5x + 1 Derivative of the Natural Exponential Function
From the definition of a derivative, we have that
d x e dx = limh0 3 Products and Quotients
1. Product Rule If u, v are both differentiable at x, then so is their product uv and In function notation, we have d [f (x)g(x)] dx = Examples
1 (a) Find y for y = x (x2 + ex ) (b) What is the derivative of y = (x2 + 1)(x3 + 3)? 2. Quotient Rule If u, v are differentiable at x and if v(x) = 0 then the quotient u/v is differentiable and In function notation, d dx f (x) g(x) = 4 Examples
(a) Find the derivative of y =
t2 1 t2 +1 (b) Find dy/dx of y = ex (c) What is the derivative of y = Rule? (x1)(x2 2x) ? x4 Do you have to use the Quotient 5 ...
View
Full
Document
 Spring '08
 FBHinkelmann
 Calculus, Derivative, Power Rule, Quotients, differentiable function, differentiable functions, Constant Multiple Rule

Click to edit the document details