# Question #5d128

##### 1 Answer

Assuming

(1)

To do this problem, you need to focus each part of the equation to differentiate before putting them together. So, let's start with

We know that according to the **power rule**, you would bring the power down to multiply the function, and then subtract by one on the exponent. For example, if you have

(2)

However, in this case we only have some constant variable c, so the exponent would be

(3)

In addition, we also need to do the **chain rule**, which states that you take a derivative on the inner function to multiply by the outer function. Since cos(t) is the inner function, the total derivative of

(4)

Finally, with the first part *implicit differentiation*, but I am going to convert this function to natural e base that equals the function:

(5)

This makes it easier to take a derivative, since any derivative of natural e base equals its anti-derivative. However, we need to take the chain rule to get the complete derivative and simplify, as shown in the step-by-step procedure:

Now that the parts we need to differentiate are complete, we can then substitute them back and get the derivative of the original function equaling Eq. 1.