Finding Particular Steps of Derivation

Thread starter eskie
Start date Nov 23, 2010
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Derivation Particular solution

In summary, to find the first step of derivation, set the derivative equal to 0 and solve for the variable. Implicit differentiation is used when the function is not given explicitly, while explicit differentiation is used when the function is given explicitly. The second step of derivation can be found by taking the derivative of the first step, and the chain rule is used when the function is composed of multiple functions. To check your work, you can use derivative rules and formulas, or online calculators and graphing software.

Nov 23, 2010

eskie

Find the Particular Solution. Show the steps of derivation, beginning w/ the general solution.
y'=y/x+(2x³/y)cos(x²),y(sqr(pi/2))=sqr(pi)

legend:
sqr=square root
pi= pi.. the 3.1416

i nid the steps.. thanks... :)

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Nov 23, 2010

Matthew Rodman

This is a simple Bernoulli equation. You may want to google it's solution, or refer to any Calc textbook.

1. How do I find the first step of derivation?

The first step of derivation can be found by setting the derivative equal to 0 and solving for the variable. This will give you the critical point or points where the derivative is equal to 0.

2. What is the difference between implicit and explicit differentiation?

Implicit differentiation is used when the function is not given explicitly in terms of the independent variable, while explicit differentiation is used when the function is given explicitly in terms of the independent variable.

3. How do I find the second step of derivation?

The second step of derivation can be found by taking the derivative of the first step, which is the critical point(s) found in the first step. This will give you the second derivative, which can determine the concavity of the function.

4. What is the chain rule and when is it used in finding particular steps of derivation?

The chain rule is used when the function is composed of two or more functions, and it helps to find the derivative of the composite function. It is used in finding particular steps of derivation when the function has nested functions or multiple functions within it.

5. How can I check my work when finding particular steps of derivation?

You can check your work by using the derivative rules and formulas to simplify your final answer and make sure it matches the original function. You can also use online derivative calculators or graphing software to verify your results.