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d/dx cosec(x) = - cosec(x) * cot(x) so the second derivative or d(d/dx)/dx cosec(x) = [- cosec(x) * d/dx cot(x)] + [ - d/dx cosec(x) * cot(x)] = [- cosec(x) * -cosec^2(x)] + [ - (- cosec(x) * cot(x)) * cot(x)] = cosec(x) * cosec^2(x) + cosec(x)*cot^2(x) = cosec(x) * [cosec^2(x) + cot^2(x)].

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0The Geometrical meaning of the second derivative is the curvature of the function. If the function has zero second derivative it is straight or flat.

All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2

The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.

well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.

2x is the first derivative of x2.

Yes.

2x is the first derivative of x2.

Afetr you take the first derivative you take it again Example y = x^2 dy/dx = 2x ( first derivative) d2y/dx2 = 2 ( second derivative)

the second derivative at an inflectiion point is zero

No. A quadratic equation always has a second derivative that is a constant. For example -3x2 + 10x - 2 first derivative -6x + 10 second derivative -6

The same way you get the second derivative from any function. Assuming you have a function that expresses potential energy as a function of time, or perhaps as a function of position, you take the derivate of this function. This will give you another function. Then, you take the derivate of this derivative, to get the second derivative.

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

Acceleration

The highest order of derivative is 2. There will be a second derivative {f''(x) or d2y/dx} in the equation.

Write sec x as a function of sines and cosines (in this case, sec x = 1 / cos x). Then use the division formula to take the first derivative. Take the derivative of the first derivative to get the second derivative. Reminder: the derivative of sin x is cos x; the derivative of cos x is - sin x.

-1/x2

2x

-4x^-2

If the second derivative of a function is zero, then the function has a constant slope, and that function is linear. Therefore, any point that belongs to that function lies on a line.

When the first derivative of the function is equal to zero and the second derivative is positive.

1/sin x = csc x

The "double prime", or second derivative of y = 5x, equals zero. The first derivative is 5, a constant. Since the derivative of any constant is zero, the derivative of 5 is zero.

Acceleration can be described as the time derivative of velocity or speed or the second time derivative of distance or displacement.

y"+y'=0 is a differential equation and mean the first derivative plus the second derivative =0.Look at e-x the first derivative is -e-xThe second derivative will be e-xThe sum will be 0

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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