00:01
In this problem we are provided with the function g of t which equals to 5 times t raised to the power 7 times e raised to the part t plus 7 times sine of t times cos of t and we are asked to differentiate this function.
00:22
So in order to differentiate this function let us look at a few rules of differentiation.
00:29
So the first one is the product rule.
00:33
So according to the product rule of differentiation, if we need to differentiate the product of two functions, we differentiate them using u v prime plus vu prime.
00:47
That is, we differentiate one at a time.
00:49
Next, the derivative of t -rays to the power n is n times t -raise to the power n minus 1.
00:58
The derivative of e raised to the part t is e raised to the part t itself.
01:03
Next, the derivative of a sign of t is cause of t, whereas the derivative of cost of t is negative sign of t.
01:14
So using these formulae, we can differentiate g of t.
01:18
We have g prime of t to be equal to...