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Q: How do you compute the derivative of the given function g of t equals 2 divided by t and t equals 1 divided by 2?

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you have to first find the derivative of the original function. You then make the derivative equal to zero and solve for x.

Because the derivative of e^x is e^x (the original function back again). This is the only function that has this behavior.

Following the correct order of operations: derivative of x^2 + 6/2 = derivative of x^2 +3, which equals 2x

1 divided by x to the third power equals x to the negative third. The derivative of x to the negative third is minus three x to the negative fourth.

The "critical points" of a function are the points at which the derivative equals zero or the derivative is undefined. To find the critical points, you first find the derivative of the function. You then set that derivative equal to zero. Any values at which the derivative equals zero are "critical points". You then determine if the derivative is ever undefined at a point (for example, because the denominator of a fraction is equal to zero at that point). Any such points are also called "critical points". In essence, the critical points are the relative minima or maxima of a function (where the graph of the function reverses direction) and can be easily determined by visually examining the graph.

pi divided by 6 is a constant and so its first derivative is 0. And since that is also a constant, the second derivative is 0. It is not clear what f(x) = csc(x) has to do with that!

Yes.

Yes, the derivative of xi with respect to x equals i. Is that what you were trying to ask?

True

29

In this case, you'll need to apply the chain rule, first taking the derivative of the tan function, and multiplying by the derivative of 3x: y = tan(3x) ∴ dy/dx = 3sec2(3x)

13

The derivative of 10x is 10. This is irrespective of the value of x.

When you solve for the 2nd derivative, you are determining whether the function is concave up/down. If you calculated that the 2nd derivative is negative, the function is concave down, which means you have a relative/absolute maximum, given that the 1st derivative equals 0. To understand why this is, think about the definition of the 2nd derivative. It is a measure of the rate of change of the gradient. At a maximum, the gradient starts positive, becomes 0 at the maximum itself and then becomes negative, so it is decreasing. If the gradient is going down, then its rate of change, the 2nd derivative, must be negative.

The intervals are determined by when the derivative is positive or negative, because the derivative is the slope and a negative slope means the function is decreasing. The function y=(x/sqrt(x2))+1, however, can be rewritten as y=x/absolutevalue(x) + 1, and as such will be represented as a pair of parallel lines, y=0 for x<0 and y=2 for x>0. As the lines are horizontal, the function is never increasing or decreasing.

x = 10x, so derivative = 10

The derivative of cos(x) equals -sin(x); therefore, the anti-derivative of -sin(x) equals cos(x).

1 divided by 13 equals 13

If 6a divided by 2 equals 12 then A equals

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.

Total annual income divided by 12 equals 1 month pay To compute annual income.... For hourly paid....at full time (40 hours a week) Hourly rate times 2080 hours equals annual payFor Salary on biweekly... salary times 26 equals annual pay

Find the derivative of Y and then divide that by the derivative of A

200 divided my 40 equals = 5

200 divided 40 equals = 5

A lot of answers... for example, 49 divided 7 equals 7.