Given that y=2x^5+(6)/(sqrt (x)),xgt 0 find in their simplest form (a) (dy)/(dx) (b) int ydx

Question

Answer 1

(a) First, we determine the derivative of the function

. This involves applying the power rule for differentiation, which states that the derivative of

is

.The derivative of

is

and the derivative of

is

.(b) Next, we calculate the integral of the function

. The integration rule states that the integral of

is

provided

.Finding the integral of

gives

, and the integral of

is

.It leaves us to add a constant of integration, which we denote as

.

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