00:01
In the question, we have to first define the chain rule.
00:07
So note that if f and g are the differentiable function, if f and g both differentiable function, and f of x is the composite function which is defined by f of x is equal to f of g of g of g of then f is differentiable and f -dash is given by the product that is f -dash -of -s is equal to f -dash -of -x times derivative of g of x so by using the chain rule we will first find the derivative of f of x is equal to f -of -x is equal to e to the power 2x.
01:18
So differentiating it, we get f -dash -of -x is equal to derivative of e to the power 2x.
01:28
That is we have f -dash of x is equal to e to the power 2x times derivative of 2 times x.
01:36
So we have f -dash of x is equal to e to the power 2x times 2, which is a required derivative by using the chandroth.
01:47
Next we have to find the derivative of function f of x which is given as log of 2 times x squared plus 4.
01:57
So we have f dash of x derivative of log of 2x square plus 4 will be 1 over 2x square plus 4.
02:07
Then we have to take the derivative of 2 times x square plus 4.
02:11
Therefore we have f -dash of x is equal to 4 times x over 2 times x squared plus 4, which is a required answer for the second function.
02:25
Now in the third, we have to find the derivative of function f of x is equal to quart of 3 times x square.
02:34
Note that the derivative of 4x is equal to negative cosec square x...