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

View Full Material##### School: University of California - Los Angeles

##### Department: Life Science

##### Course: Life Sciences 30A - Mathematics for Life Scientists

##### Professor: W.j. Conley

##### Term: Winter 2019

##### Tags: Math and Calculus

##### Name: Life Science 30A Notes Week 5

##### Description: These notes cover what was discussed in class during Week 5.

##### Uploaded: 02/08/2019

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**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 2

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##### School: University of California - Los Angeles

##### Department: Life Science

##### Course: Life Sciences 30A - Mathematics for Life Scientists

##### Professor: W.j. Conley

##### Term: Winter 2019

##### Tags: Math and Calculus

##### Name: Life Science 30A Notes Week 5

##### Description: These notes cover what was discussed in class during Week 5.

##### Uploaded: 02/08/2019

**2**Pages

**71**Views

**56**Unlocks

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