3.7 Implicit Differentiation. Niagara Falls, NY & Canada. Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. F4. F3. 2. On the sending unit, press , and then . . 2nd. VAR-LINK. 2nd.

ByPhoto by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. 7.3 day 2. Disk and Washer Methods. Limerick Nuclear Generating Station, Pottstown, Pennsylvania. Suppose I start with this curve.

By8.2 Relative Rates of Growth. Greg Kelly, Hanford High School, Richland, Washington. At 64 inches, the y-value would be at the edge of the known universe! (13 billion light-years). The function grows very fast. We could graph it on the chalkboard: .

ByPhoto by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. 3.2 Differentiability. Arches National Park. Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. Arches National Park.

ByPhoto by Vickie Kelly, 2004. Greg Kelly, Hanford High School, Richland, Washington. 7.5 part 1 Work and Pumping Liquids. Hoover Dam Nevada & Arizona. Photo by Vickie Kelly, 2004. Greg Kelly, Hanford High School, Richland, Washington. Hoover Dam Powerhouse Nevada & Arizona.

By6.4 Exponential Growth and Decay. Glacier National Park, Montana Photo by Vickie Kelly, 2004. Greg Kelly, Hanford High School, Richland, Washington.

ByPhoto by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. 3.3 Rules for Differentiation. Colorado National Monument. The derivative of a constant is zero. If the derivative of a function is its slope, then for a constant function, the derivative must be zero.

ByPhoto by Greg Kelly, 2005. Greg Kelly, Hanford High School, Richland, Washington. 1.4 Parametric Equations. Mt. Washington Cog Railway, NH. We can do this by writing equations for the x and y coordinates in terms of a third variable (usually t or ).

ByPhoto by Vickie Kelly, 2007. Greg Kelly, Hanford High School, Richland, Washington. Mt. Rushmore, South Dakota. 3.9: Derivatives of Exponential and Logarithmic Functions. Look at the graph of . If we assume this to be true, then:. The slope at x=0 appears to be 1. definition of derivative.

By8.3 Relative Rates of Growth. Greg Kelly, Hanford High School, Richland, Washington. At 64 inches, the y-value would be at the edge of the known universe! (13 billion light-years). The function grows very fast. We could graph it on the chalkboard: .

ByPhoto by Vickie Kelly, 1993. Greg Kelly, Hanford High School, Richland, Washington. 2.4 Rates of Change and Tangent Lines. Devil’s Tower, Wyoming. The slope of a line is given by:. The slope at (1,1) can be approximated by the slope of the secant through (4,16).

ByPhoto by Vickie Kelly, 2007. Greg Kelly, Hanford High School, Richland, Washington. 4.6: Related Rates. Olympic National Park, Washington. Photo by Vickie Kelly, 2007. Greg Kelly, Hanford High School, Richland, Washington. 4.6: Related Rates. Olympic National Park, Washington.

Byz. 100. An Introduction to Partial Derivatives. 10. y. 10. x. Greg Kelly, Hanford High School, Richland, Washington. When we have functions with more than one variable, we can find partial derivatives by holding all the variables but one constant. z. 100. 10. y. 10. x.

ByPhoto by Vickie Kelly, 1999. Greg Kelly, Hanford High School, Richland, Washington. 7.4 Day 1 Lengths of Curves. Golden Spike National Historic Site, Promontory, Utah. Length of Curve (Cartesian). Lengths of Curves:.

By7.4 Day 2 Surface Area. (Photo not taken by Vickie Kelly). Greg Kelly, Hanford High School, Richland, Washington. r. Surface Area about x -axis (Cartesian):. To rotate about the y -axis, just reverse x and y in the formula!. Surface Area:.

By9.2 day 2. Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. Maclaurin Series. Liberty Bell, Philadelphia, PA. Maclaurin Series:. (generated by f at ).

By9.2 day 2. Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. Finding Common Maclaurin Series. Liberty Bell, Philadelphia, PA. Maclaurin Series:. (generated by f at ).

By8.2 Day 2: Identifying Indeterminate Forms. Photo by Vickie Kelly, 2008. Greg Kelly, Hanford High School, Richland, Washington. Brooklyn Bridge, New York City. What makes an expression indeterminate?. Consider:. We can hold one part of the expression constant:.

ByPhoto by Vickie Kelly, 1999. Greg Kelly, Hanford High School, Richland, Washington. 4.4 Modeling and Optimization. Buffalo Bill’s Ranch, North Platte, Nebraska. There must be a local maximum here, since the endpoints are minimums. A Classic Problem.

ByPhoto by Vickie Kelly, 1993. Greg Kelly, Hanford High School, Richland, Washington. 3.8 Derivatives of Inverse Trig Functions. Lewis and Clark Caverns, Montana. At x = 2 :. We can find the inverse function as follows:. To find the derivative of the inverse function:. Switch x and y .

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