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UCLA - LIFESCI 30 - Life Science 30A Notes Week 5 - Class Notes

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UCLA - LIFESCI 30 - Life Science 30A Notes Week 5 - Class Notes

Description: These notes cover what was discussed in class during Week 5.
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2.3 -- Derivatives: A Geometric Interpretation    - secant line ​: a straight line through a curve defined by slope Δy/Δx, representing average  rate of change  - slope of a secant line = average rate of change  - tangent line ​: intersects the curve at just one point as Δx → 0, the limit of the secant  process  - slope of a tangent line = instantaneous rate of change  - point-slope form ​: (y - y​ 0 ) = m(x - x 0

2.4 -- Derivatives: Linear Approximation    - linear function conditions ​:   - f(x 1 +x 2 ) = f(x 1 ) + f(x 2 - f(ax) = af(x)  - linear approximation function ​: f(x) = f(x​ 0 ) + f’(x 0 )*(x-x 0 ) or Δf = f’(x 0 )*Δx  - differentiability ​: a function is differentiable at a point if it has a derivative at that point  - In order to be differentiable, it must;  1. be continuous at that point
2. not have a cusp or corner at that point
3. not have a vertical tangent at that point

2.5 -- The Derivative of a Function    - higher order derivative ​: taking the derivative of a derived function  - derivative rules ​:   - constant (c) ​: d/dx(c) = 0  - power functions ​: d/dx(x​ n ) = nx n-1  - exponential functions ​: d/dx(e​ kx ) = ke kx  - logarithmic functions ​: d/dx(lnx) = 1/x  - trigonometric functions ​: d/dx(sin(x)) = cos(x)      d/dx(cos(x)) = -sin(x)  - constant multiple rule ​: dh/dx = d(c*f)/dx = c*df/dx  - addition rule ​: dh/dx = d(f+g)/dx = df/dx + dg/dx  - product rule ​: dh/dx = d(f*g)/dx = df/dx*g+f*dg/dx  - quotient rule ​: dh/dx = d(f/g)/dx = ((df/dg)*g - (dg/dx)*f)/g​

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Description: These notes cover what was discussed in class during Week 5.
2 Pages 71 Views 56 Unlocks
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