Differentiate each of the following functions.i. y = 5x9 + 10ii. y = x3/5iii. y = 12e2x+4iv. y = ln(9x)

Sure, here are the derivatives of the given functions:

i. The derivative of y = 5x^9 + 10 is dy/dx = 45x^8. This is obtained by applying the power rule which states that the derivative of x^n is n*x^(n-1).

ii. The derivative of y = x^(3/5) is dy/dx = (3/5)x^(-2/5). Again, this is obtained by applying the power rule.

iii. The derivative of y = 12e^(2x+4) is dy/dx = 24e^(2x+4). This is obtained by applying the chain rule which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

iv. The derivative of y = ln(9x) is dy/dx = 1/x. This is obtained by applying the rule that the derivative of ln(x) is 1/x.