Best Answer

I've heard what I'm going to tell you called the "power rule" before. It's the only thing I've ever heard referred to as the power rule.

It's simply the way to find the derivative of a polynomial function, something of the form:

y=axn

where a and n are any real number

The power rule states that to find the derivative (y-prime (y')) of any function of this type, you simply follow this format:

y'=an*xn-1

following this format to higher derivatives:

y''=(a)(n)(n-1)xn-2

y'''=(a)(n)(n-1)(n-2)xn-3

In written terms, you simply bring down the current exponent in front of the variable and lower the exponent by one to make the derivative.

For three examples:

y=6x3

y'=(6)(3)x3-1=18x2

y''=(18)(2)x2-1=36x1=36x

y'''=(36)(1)x1-1=36x0=36

y=7x-3=7/x3

y'=(7)(-3)x-3-1=-21x-4

and so on...

y=4sqrt(x)=4x1/2

y'=(4)(1/2)x(1/2)-1=2x-1/2

and so on...

The last two examples were to show that this method still works for negative exponents, fractional exponents...any exponent that is a real number.

This does not apply only to functions who are purely polynomial. Any component of a larger function that is polynomial can be derived in this way (as long as the component is added or subtracted; division or subtraction brings the product rule into play).

For example:

y=2x2+cos(x-2)

The component "2x2" has a derivative of 4x due to the power rule.

For the record:

y'=4x-sin(x-2)

Q: In calculus what is the power rule?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

The chain rule, in calculus, is a formula. It allows one to compute the derivative of the composition of two or more functions. It was first used by the German mathematician Gottfried Leibniz.

xx + sincos

Here's an example calculus question: Find lim (x^2-4)/(x^2+2x-8) using l'hopital's rule. x->2

i love wikipedia!According to wiki: In calculus, integration by substitution is a method for finding antiderivatives and integrals. Using the fundamental theorem of calculus often requires finding an antiderivative. For this and other reasons, integration by substitution is an important tool for mathematicians. It is the counterpart to the chain rule of differentiation.

Calculus; by a long shot.

Related questions

The chain rule, in calculus, is a formula. It allows one to compute the derivative of the composition of two or more functions. It was first used by the German mathematician Gottfried Leibniz.

not calculus

xx + sincos

Here's an example calculus question: Find lim (x^2-4)/(x^2+2x-8) using l'hopital's rule. x->2

compose yourselves!

The product rule is used in calculus when one is dealing with functions that are written as the product of other functions. The actual calculation will depend on the type and number of functions.

i love wikipedia!According to wiki: In calculus, integration by substitution is a method for finding antiderivatives and integrals. Using the fundamental theorem of calculus often requires finding an antiderivative. For this and other reasons, integration by substitution is an important tool for mathematicians. It is the counterpart to the chain rule of differentiation.

Any positive power of zero (0 times 0) will equal zero. But 00 is not defined in ordinary math. This is an exception to the rule x0 = 1, which applies to all nonzero numbers. In calculus, and in polynomial and power series, 00 is defined as 1, but in continuous limiting functions, x0 does not exist for zero.

Calculus; by a long shot.

power,rule,authority,influence

Pre-calculus refers to concepts that need to be learned before, or as a prerequisite to studying calculus, so no. First one studies pre-calculus then elementary calculus.

Just about all of calculus is based on differential and integral calculus, including Calculus 1! However, Calculus 1 is more likely to cover differential calculus, with integral calculus soon after. So there really isn't a right answer for this question.