this to me is like a "puzle"; like the problem "find i^15" you find a pattern w/o having to go the whole way. Same here.Mathysics said:Homework Statement
Find the first, second, third, fourth, fifth derivatives of the function y = sin 3x.
Find a rule that can help to find the 50th derivative of the function.
It's urgent!
Homework Equations
y= sin x y= cos x
y' = cos x y' = -sin x
y= sin ax y= cos ax
y' = a sin cos ax y' = -a sin ax
The Attempt at a Solution
My attempt to the question: y = -a^n sin ax for even
y = a^n cos ax for odd
Plz show steps so that i can follow, cheers
A derivative is a mathematical concept that measures the rate of change of a function with respect to its independent variable. It represents the slope of a tangent line to the function at a specific point.
To find the 50th derivative of a function, you would use the power rule and the chain rule repeatedly until you have taken the derivative 50 times. This process can be time-consuming and complex, so it is often done using computer algebra systems.
The 50th derivative of a function can provide information about the behavior and properties of the function, such as the rate of change, curvature, and inflection points. It can also be used to find the Taylor series of a function, which is a representation of the function as an infinite sum of derivatives.
In most cases, finding the 50th derivative of a function is not necessary. It is usually only done for theoretical or mathematical purposes and does not have practical applications. However, it can provide insight into the behavior of a function at a specific point.
There are no shortcuts or tricks to finding the 50th derivative of a function. It requires a thorough understanding of the power rule, chain rule, and other derivative rules, as well as patience and practice. As mentioned earlier, computer algebra systems can also be used to find the derivative efficiently.