Differentiate the function f(t)=1/4(t^4+8). My answer wa 4t^3. The book says t^3. What am I doing wrong,
To differentiate the function f(t) = 1/4(t^4 + 8), you need to apply the power rule of differentiation. The power rule states that if you have a function of the form f(t) = k(t^n), where k is a constant, then the derivative is given by f'(t) = n * k * t^(n-1).
Let's differentiate the function step by step:
1. Start by differentiating the first term, t^4. The power rule tells us that the derivative of t^4 is (4 * t^(4-1)), which simplifies to 4 * t^3.
2. Next, differentiate the constant term 8. The derivative of a constant is zero, so the derivative of 8 is simply 0.
3. Now, combine the derivatives of the two terms. The derivative of t^4 is 4 * t^3, and the derivative of 8 is 0. Since (0 + 4 * t^3) is equal to 4 * t^3, the result is indeed 4 * t^3.
Therefore, your answer of 4 * t^3 is correct, and it matches the derivative obtained by applying the power rule. If the book answer says t^3, it might be a mistake. However, it's always a good idea to double-check with your teacher or consult other reliable resources to confirm.