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Why do take derivative?


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Answered 2009-11-26 10:03:04

To find rate of change.

Two common examples are:

rate of change in position = velocity and rate of change of velocity = acceleration.

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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


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 idea is to use the addition/subtraction property. In other words, take the derivative of 5x, take the derivative of 1, and subtract the results.


Trig functions have their own special derivatives that you will have to memorize. For instance: the derivative of sinx is cosx. The derivative of cosx is -sinx The derivative of tanx is sec2x The derivative of cscx is -cscxcotx The derivative of secx is secxtanx The derivative of cotx is -csc2x


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.


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.


You take the derivative of the function, then solve the inequality:derivative > 0 for increasing, orderivative


How do I take the derivative of... (58+Rpi)(500000/pi)(r^-1)+19*pi*r^2 where R is a constant


You can take out any constant from a derivative. In other words, this is the same as 5 times the derivative of sec x.


f'(x)=-sin2x(2) f'(x)=-2sin2x First do the derivative of cos u, which is -sin u. Then because of the chain rule, you have to take the derivative of what's inside and the derivative of 2x is 2.


Take the derivative of the function.


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I assume you mean 27 times e to the power x. 1) You take out the constant out. So, the derivative is 27 times the derivative of (e to the power x).2) You use the rule for the exponential function.


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Every fourth derivative, you get back to "sin x" - in other words, the 84th derivative of "sin x" is also "sin x". From there, you need to take the derivative 3 more times, getting:85th derivative: cos x86th derivative: -sin x87th derivative: -cos x


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.


A dot A = A2 do a derivative of both sides derivative (A) dot A + A dot derivative(A) =0 2(derivative (A) dot A)=0 (derivative (A) dot A)=0 A * derivative (A) * cos (theta) =0 => theta =90 A and derivative (A) are perpendicular


You can differentiate a function when it only contains one changing variable, like f(x) = x2. It's derivative is f'(x) = 2x. If a function contains more than one variable, like f(x,y) = x2 + y2, you can't just "find the derivative" generically because that doesn't specify what variable to take the derivative with respect to. Instead, you might "take the derivative with respect to x (treating y as a constant)" and get fx(x,y) = 2x or "take the derivative with respect to y (treating x as a constant)" and get fy(x,y) = 2y. This is a partial derivative--when you take the derivative of a function with many variable with respect to one of the variables while treating the rest as constants.


Write it as (1/3)x and take the derivative. You get (1/3)x0 = 1/3 * 1 = 1/3 ■


We always take the first derivative of ESR spectra in electron paramagnetic resonance spectroscopy to get sufficient signal to noise.


The derivative of e7x is e7 or 7e.The derivative of e7x is 7e7xThe derivative of e7x is e7xln(7)


Velocity is the derivative of position.Velocity is the derivative of position.Velocity is the derivative of position.Velocity is the derivative of position.


Consider that a sawtooth waveform is the summation of the infinite series of sine waves with amplitude equal to 1 over the multiplier of the frequency. Now you can take the derivative, or at least approximate it. You will find that the derivative of a sawtooth is a pulse, in the ideal case, a pulse with infinite amplitude and zero width.



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