Question

Hello please can you help me with the equation find the derivative of the function

Answer 1

You have the following expression:

`f(t)=(5t^2+1)(2\sqrt[]{t}-3t+1)`

In order to derivate the previous function, notice that you have a product between two factors, then, by using the derivative of a product you obtain:

`f^(\prime)(t)=(5t^2+1)^(\prime)(2\sqrt[]{t}-3t+1)+(5t^2+1)(2\sqrt[]{t}-3t+1)^(\prime)`

Now, the derivatives of the factors are:

`\begin{gathered} (5t^2+1)^(\prime)=10t \\ (2\sqrt[]{t}-3t+1)^(\prime)=(2t^{(1)/(2)}-3t+1)^(\prime)=t^{-(1)/(2)}-3 \end{gathered}`

Then, by replacing the previous expressions into f'(t):

`f^(\prime)(t)=10t(2t^{(1)/(2)}-3t+1)+(5t^2+1)(t^{-(1)/(2)}-3)`

The previous expression is the result for the derivative of f(t).