what is the power of a power rule The power of a power rule is an important exponent rule law of exponent used to simplify an expression of the form x m n where the base x is raised to a power m and the entire expression x m is raised to the power n again
The power rule helps us find the derivative of functions and expressions raised to a power We ll explore how this particular derivative rule was derived and understand why we need to establish a power rule for expressions with a higher power The power of a power rule f 2 5 f 10 applies whether the powers are positive negative variables or fractions In a negative power the base is rewritten as the
what is the power of a power rule
what is the power of a power rule
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Power Of A Power Worksheet Rules And Definition
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Power Of Power Exponent Rule
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The Power Rule for Powers The following examples suggest a rule for raising a power to a power a 2 3 a 2 cdot a 2 cdot a 2 Using the product rule we get a 2 3 a 2 2 2 a 2 3 a 3 cdot 2 a 2 3 a 6 x 9 4 x 9 cdot x 9 cdot x 9 cdot x 9 x 9 4 x 9 9 9 9 x 9 4 x 4 cdot 9 x 9 The Power Rule one of the most commonly used derivative rules says The derivative of xn is nx n 1 Example What is the derivative of x 2 For x 2 we use the Power Rule with n 2 Answer the derivative of x2 is 2x The derivative of can be shown with this little dash mark Using that mark we can write the Power Rule like this
Power of a Quotient Rule Let a and b be a positive real numbers and n be any real number Then left dfrac a b right n dfrac a n b n nonumber In calculus the power rule is the following rule of differentiation Power Rule For any real number c frac d dx x c c x c 1 Using the rules of differentiation and the power rule we can calculate the derivative of polynomials as follows Given a polynomial f x a nx n a n 1 x n 1 cdots a 1x a 0
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We can raise exponential to another power or take a power of a power The result is a single exponential where the power is the product of the original exponents begin gather x a b x ab label power power end gather Contributors We start with the derivative of a power function f x x n Here n is a number of any kind integer rational positive negative even irrational as in x pi We have already computed some simple examples so the formula should not be a complete surprise d over dx x n nx n 1
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what is the power of a power rule - Power of a Quotient Rule Let a and b be a positive real numbers and n be any real number Then left dfrac a b right n dfrac a n b n nonumber