Question

Find the derivative. s=t^6tan(t)-sqrt t

Answer 1

If you mean t^6 tan t - √t
just use the product rule on the first term:

ds/dt = 6t^5 tan t + t^6 sec^2 t - 1/(2√t)

That can be massaged in various ways:

t^5(6tan t + t sec^2 t)
t^5(t tan^2 t + 6tan t + t) - 1/2√t

Answer 2

s = t^6 * tan(t) - sqrt(t)

ds/dt = t^6 (sec^2 (t)) + 6t^5 (tan(t)) - (1/2)(1/sqrt(t))

Answer 3

correct