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(x3)'=3x2

(x3)''=(3x2)'=6x

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Q: What is the second derivative of 1xto the power 3?
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What is the second derivative of x to the fourth power?

d/dx(X^4) = 4X^3 ( first derivative ) d/dx(4X^3) = 12X^2 ( second derivative )


What is the second derivative of the square root of x to the power of 3?

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Find the second derivative for the square root of x2 - 3?

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Is there a sequence to finding multiple derivatives of the square root of x?

sqrt(X) is also X^1/2 use power rule 1/2X^-1/2 ( first derivative ) -1/4X^-3/2 ( second derivative ) and so on


What is the derivative of 40u to the fifth power divided by 5u to the second power with respect to u?

24u to the second power. Differentiate 40u to the fifth power which is 200u to the fourth power and 5u to the second power which is 10u. Subtract 400u to the sixth power from 1000u to the sixth power which is 600u to the sixth power. Then square 5u to the second power which is 25u to the fourth power. Finally, divide 600u to the sixth power by 25u to the fourth power. The solution is 24u to the second power. Another method is simplifying it to 8u cubed (to the third power) and taking the power rule. Take 3 times 8u which is 24u and subtract 1 from 3 in exponent which is 2. The answer is 24u to the second power.


What is the Order of a differential equation?

The order of a differential equation is a highest order of derivative in a differential equation. For example, let us assume a differential expression like this. d2y/dx2 + (dy/dx)3 + 8 = 0 In this differential equation, we are seeing highest derivative (d2y/dx2) and also seeing the highest power i.e 3 but it is power of lower derivative dy/dx. According to the definition of differential equation, we should not consider highest power as order but should consider the highest derivative's power i.e 2 as order of the differential equation. Therefore, the order of the differential equation is second order.


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The derivate of 3x is 3; the derivative of -1 is 0. So, the derivative of 3x-1 is simply 3.The derivate of 3x is 3; the derivative of -1 is 0. So, the derivative of 3x-1 is simply 3.The derivate of 3x is 3; the derivative of -1 is 0. So, the derivative of 3x-1 is simply 3.The derivate of 3x is 3; the derivative of -1 is 0. So, the derivative of 3x-1 is simply 3.


What is the third derivative of lnx?

The first derivative of ln x is 1/x, which (for the following) you better write as x-1.Now use the power rule:Second derivative (the derivative of the first derivative) is -1x-2, the third derivative is the derivative of this, or 2x-3. You may now wish to write this in the alternative form, as 2 / x3.


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