- #1
amac1212
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Homework Statement
- 8 - sqr(29-4x+x^2)
Homework Equations
The Attempt at a Solution
-8(-1/2)=4
4(29-4x+x^2)^-1/2(2x-4)?
am i on the right track?
The derivative of the function is -4x/(29-4x+x^2).
To find the derivative of a function, you need to use the rules of differentiation, such as the power rule, product rule, and chain rule. The derivative of a function is the slope of its graph at any given point.
The derivative plays a crucial role in calculus because it helps us understand how a function changes over time or distance. It also helps us to optimize functions and find the maximum and minimum values.
The power rule states that the derivative of a function with a constant raised to a power is equal to the constant multiplied by the power, and the power reduced by one. In other words, d/dx (x^n) = nx^(n-1).
Derivatives have various real-life applications, such as in physics to calculate the velocity and acceleration of an object, in economics to determine the rate of change of a function, and in engineering to optimize designs and systems. They are also used in finance to calculate the rate of return on investments and in medicine to analyze data from medical tests.