Question

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)=

Answer 1

(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

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