Enter the function u, its power n, and the derivative of u with respect to x into the calculator to determine the derivative using the Generalized Power Rule.
Generalized Power Rule Formula
The following formula is used to calculate the derivative using the Generalized Power Rule.
d/dx [u^n] = n*u^{(n-1)}*u'Variables:
- d/dx [u^n] is the derivative of the function u^n with respect to x
- u is a differentiable function of x
- n is a real number (the power to which u is raised)
- u’ is the derivative of u with respect to x
To calculate the derivative using the Generalized Power Rule, first identify the function u and its power n. Then, calculate the derivative of u with respect to x (u’). Multiply the power n by the function u raised to the power of n-1, and then multiply this result by u’. This gives the derivative of the function u^n with respect to x.
What is a Generalized Power Rule?
The Generalized Power Rule is a formula used in calculus to differentiate functions that are in the form of a power of a function. It is an extension of the basic power rule in calculus and is used when the exponent is not necessarily a constant but a function of the variable. The rule states that the derivative of u^n, where u is a differentiable function of x and n is a real number, is n*u^(n-1)*u’, where u’ is the derivative of u with respect to x.
How to Calculate Generalized Power Rule?
The following steps outline how to calculate the derivative of a function using the Generalized Power Rule.
- First, identify the function u and the power n.
- Next, differentiate the function u with respect to x to find u’.
- Then, apply the Generalized Power Rule formula: d/dx [u^n] = n*u^(n-1)*u’.
- Finally, substitute the values of u, n, and u’ into the formula and simplify the expression.
- After simplifying, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
u = 3x^2
n = 4
u’ = 6x
