Differentiate the following function.
f(t) = 6/7t^6 − 7^t4 + 4t
Differentiate the following function.
f(t) = 6/7t^6 − 7t^4 + 4t
Enough already. Try some yourself.
Did this in 1955, do not need practice.
Ben, Kevin, can you please post work along with your questions? This will help our tutors determine where you are getting stuck. Thanks!
To differentiate the function f(t) = 6/7t^6 - 7t^4 + 4t, we need to take the derivative with respect to t.
The derivative of a function is the rate at which the function is changing with respect to its independent variable. In this case, we want to find how the function f(t) changes as t changes.
To differentiate the given function, we use the power rule and the constant rule of differentiation. Here's how you can do it step by step:
Step 1: Apply the power rule to each term separately.
The power rule states that if we have a term of the form kt^n, then its derivative is given by nkt^(n-1).
For the first term 6/7t^6, the derivative is:
(6/7)(6)t^(6-1) = 36/7t^5
For the second term -7t^4, the derivative is:
(-7)(4)t^(4-1) = -28t^3
For the third term 4t, the derivative is simply 4.
Step 2: Combine the derivatives of each term to get the derivative of the entire function.
The derivative of the function f(t) = 6/7t^6 - 7t^4 + 4t is:
36/7t^5 - 28t^3 + 4
So, the differentiation of the given function is:
f'(t) = 36/7t^5 - 28t^3 + 4