Finding the Derivative of 2sin(x) - 5e^x

Thread starter BuBbLeS01
Start date Nov 16, 2007
Tags

Integrating

In summary, the function 2sin(x) - 5e^x is a combination of a sine function and an exponential function that is used to model various natural phenomena. To graph 2sin(x) - 5e^x, the individual functions are first graphed and then their corresponding y-values are added or subtracted. The important features of the graph include x-intercepts, maximum and minimum points, period, amplitude, and rate of growth/decay. The derivative of the function can be calculated using the rules of differentiation. Real-world applications of 2sin(x) - 5e^x include modeling the movement of a pendulum, spring behavior, and population growth/decay, as well as data analysis in

Nov 16, 2007

BuBbLeS01

Homework Statement

(2sinx - 5e^x)

The Attempt at a Solution

is it just...
-2cosx - 5e^x

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Nov 16, 2007

Dick

Science Advisor

Homework Helper

Well, yes. Plus an integration constant. Why would you think otherwise?

Nov 16, 2007

BuBbLeS01

I don't know...I always second guess myself so I love reassurance...thank you!

1. What is the function of 2sin(x) - 5e^x?

The function 2sin(x) - 5e^x is a combination of a sine function and an exponential function. It is used to model many natural phenomena, including periodic oscillations and growth/decay processes.

2. How do you graph 2sin(x) - 5e^x?

The graph of 2sin(x) - 5e^x can be plotted by first graphing the individual functions of sin(x) and e^x, and then adding or subtracting their corresponding y-values at each point on the x-axis.

3. What are the important features of the graph of 2sin(x) - 5e^x?

The important features of the graph of 2sin(x) - 5e^x include the x-intercepts, where the function crosses the x-axis, and the maximum and minimum points, where the function reaches its highest and lowest values. The period and amplitude of the sine function and the rate of growth/decay of the exponential function can also be observed on the graph.

4. How is the derivative of 2sin(x) - 5e^x calculated?

The derivative of 2sin(x) - 5e^x can be calculated using the rules of differentiation. The derivative of sin(x) is cos(x) and the derivative of e^x is e^x, so the derivative of the entire function is 2cos(x) - 5e^x.

5. What real-world applications does 2sin(x) - 5e^x have?

The function 2sin(x) - 5e^x has many real-world applications, including modeling the movement of a pendulum, the behavior of a spring, and the growth/decay of populations in biology. It can also be used to analyze data in fields such as economics and engineering.