Question

Differentiate the function f(t)=t⁸e⁸ with respect to t.

a) 8t⁷e⁸
b) 8t⁸e⁷
c) 64t⁷e⁸
d) t⁸e⁸

Answer 1

To differentiate the function f(t) = t⁸e⁸ with respect to t, use the product rule. The derivative of f(t) is 8t⁷e⁸.

Step-by-step explanation:

To differentiate the function f(t) = t⁸e⁸ with respect to t, we can use the product rule. The product rule states that if we have two functions u(t) and v(t), then the derivative of the product of u(t) and v(t) is given by (u(t)v'(t) + u'(t)v(t)).

Applying the product rule in this case, we have:

f'(t) = (t⁸)'e⁸ + t⁸(e⁸)'

The derivative of t⁸ with respect to t is 8t⁷, and the derivative of e⁸ with respect to t is 0, because e⁸ is a constant. Therefore, the derivative of f(t) is:

f'(t) = 8t⁷e⁸