To solve, simply differentiate  using the power rule to find .  Then plug in  for . 

Recall the power rule:

Apply this to get

To solve, simply differentiate using the power rule and then plug in . Recall the power rule:

Thus,

Acceleration of a particle can be found by taking the derivative of the velocity function with respect to time. Recall that a derivative gives the rate of change of some parameter, relative to the change of some other variable. When we take the derivative of velocity with respect to time, we are evaluating how velocity changes over time; i.e acceleration! This is just like finding velocity by taking the derivative of the position function.

For 

Using the above properties, the velocity function is

And the acceleration function is

At time 

Acceleration of a particle can be found by taking the derivative of the velocity function with respect to time. Recall that a derivative gives the rate of change of some parameter, relative to the change of some other variable. When we take the derivative of velocity with respect to time, we are evaluating how velocity changes over time; i.e acceleration! This is just like finding velocity by taking the derivative of the position function.

To take the derivative of the function

We'll need to make use of the following derivative rule(s):

Trigonometric derivative: 

Quotient rule: 

Note that u and v may represent large functions, and not just individual variables!

Using the above properties, the velocity function is

And the acceleration function is

At time 

Acceleration of a particle can be found by taking the derivative of the velocity function with respect to time. Recall that a derivative gives the rate of change of some parameter, relative to the change of some other variable. When we take the derivative of velocity with respect to time, we are evaluating how velocity changes over time; i.e acceleration! This is just like finding velocity by taking the derivative of the position function.

To take the derivative of the function

We'll need to make use of the following derivative rule(s):

Trigonometric derivative: 

Quotient rule: 

Note that u and v may represent large functions, and not just individual variables!

Using the above properties, the velocity function is

And the acceleration function is

To find the bug's initial acceleration, we must find the accleration function, which is the second derivative of the position function:

The following rules were used to find the derivatives:
, , 

Finally, since we were asked about the bug's initial acceleration, we simply plug in t=0 into the acceleration function:

To find the acceleration function, you have to first find the velocity function, which means taking the derivative of the position function. To take the derivative of a function, multiply the exponent by the coefficient in front of an  and then subtract the exponent by . Therefore, the velocity function is: . Then, to find the acceleration, take the derivative of the velocity function. Therefore, your answer is:

The first step here is to find the velocity function. To do that, you must find the derivative of the position function. Remember, when taking the derivative, multiply the exponent by the coefficient in front of the  term and then subtract one from the exponent. Therefore, the velocity function is: . Then, to find the acceleration function, take the derivative of velocity. The answer is then: .

In order to find the acceration of an object in a plane at any give point , you must first differentiate the first derivative.

In this case, the first derivative is:

When you differentiate the first derivative, you get the second derivative:  

Therefore, the correct answer is .

In order to find the acceration of an object in a plane at any give point , you must first differentiate the first derivative.

In this case, the first derivative is: 

When you differentiate the first derivative, you get the second derivative:  

This is the function that gives you the acceleration of an object vector at point .

You plug  into the second derivative and therefore, the correct answer is .