lecture11 - Section 3.2: Derivative Rules Powers,...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the 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 , xn-1 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 = e-x (c) What is the derivative of y = Rule? (x-1)(x2 -2x) ? x4 Do you have to use the Quotient 5 ...
View Full Document

Page1 / 5

lecture11 - Section 3.2: Derivative Rules Powers,...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online