Calculate the following derivatives. Assume y is a function of t. Use Y for the derivative of y. (a) d dt y7 = Incorrect: Your answer is incorrect. (b) d dt y3e4t = Incorrect: Your answer is incorrect. (c) d dt t7 cos (y6) =

(a) d dt y7=7Y^6

(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}

(c) d dt t7 cos (y6) = 7t^6 cos (y6) + t^7 (-sin (y^6)) ·6Y^5

Step-by-step explanation:

We calculate the following derivatives. Since these are complex derivatives, we also calculate the formula for complex derivatives. We use Y for the derivative of y. Therefore, we calculate and we get

(a) d dt y7=7Y^6

(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}

(c) d dt t7 cos (y6) = 7t^6 cos (y6) + t^7 (-sin (y^6)) ·6Y^5