Question

"Find the derivative. d′(t)=5cos2t" is already a derivative expression. To find the original function d(t) from this derivative, you would need to perform the reverse operation, which is integration. You can integrate 5cos2t to find d(t)

Answer 1

To find the original function d(t) from the given derivative expression d'(t) = 5cos²(t), we need to perform the reverse operation, which is integration. We can integrate 5cos²(t) to find d(t).

Step-by-step explanation:

To find the original function d(t) from the given derivative expression d'(t) = 5cos²(t), we need to perform the reverse operation, which is integration. We can integrate 5cos²(t) to find d(t).

1. Using the trigonometric identity cos²(t) = 1/2 + 1/2cos(2t) to rewrite the expression, we have d'(t) = 5(1/2 + 1/2cos(2t)).
2. Integrating each term separately, we get d(t) = 5t/2 + 5/4sin(2t) + C, where C is the constant of integration.

Therefore, the original function d(t) is d(t) = 5t/2 + 5/4sin(2t) + C, where C is a constant.