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What is the derivative for 3x to the power of -1?

Updated: 3/26/2021
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14y ago

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Charlie Schulist

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3y ago
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14y ago

If I understand correctly, your function is f(x) = (3x)-1. This is the same as 1/(3x), but as a power, it is easier to take the derivative.

You first apply the power rule: -1(3x)-2. Since you are not working with a power of "x" but another expression, you have to multiply this by the derivative of 3x, which is 3.

The derivative, then, is -1(3x)-2 x 3 = -3(3x)-2 = -(3/9)x-2 = -(1/3)x-2 = -1/(3x2)

If I understand correctly, your function is f(x) = (3x)-1. This is the same as 1/(3x), but as a power, it is easier to take the derivative.

You first apply the power rule: -1(3x)-2. Since you are not working with a power of "x" but another expression, you have to multiply this by the derivative of 3x, which is 3.

The derivative, then, is -1(3x)-2 x 3 = -3(3x)-2 = -(3/9)x-2 = -(1/3)x-2 = -1/(3x2)

If I understand correctly, your function is f(x) = (3x)-1. This is the same as 1/(3x), but as a power, it is easier to take the derivative.

You first apply the power rule: -1(3x)-2. Since you are not working with a power of "x" but another expression, you have to multiply this by the derivative of 3x, which is 3.

The derivative, then, is -1(3x)-2 x 3 = -3(3x)-2 = -(3/9)x-2 = -(1/3)x-2 = -1/(3x2)

If I understand correctly, your function is f(x) = (3x)-1. This is the same as 1/(3x), but as a power, it is easier to take the derivative.

You first apply the power rule: -1(3x)-2. Since you are not working with a power of "x" but another expression, you have to multiply this by the derivative of 3x, which is 3.

The derivative, then, is -1(3x)-2 x 3 = -3(3x)-2 = -(3/9)x-2 = -(1/3)x-2 = -1/(3x2)

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User Avatar

Wiki User

14y ago

If I understand correctly, your function is f(x) = (3x)-1. This is the same as 1/(3x), but as a power, it is easier to take the derivative.

You first apply the power rule: -1(3x)-2. Since you are not working with a power of "x" but another expression, you have to multiply this by the derivative of 3x, which is 3.

The derivative, then, is -1(3x)-2 x 3 = -3(3x)-2 = -(3/9)x-2 = -(1/3)x-2 = -1/(3x2)

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Q: What is the derivative for 3x to the power of -1?
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