If y = (sin t)^5t , find dy/dx.

Question

If y = (sin t)^5t , find dy/dx.

Answer 1

y = (sint)^5t

 

To find y' (i.e., dy/dt) use logarithmic differentiation.

 

lny = 5t ln(sint)

 

y'/y = 5 ln(sint) + 5t (cost/sint)

 

y' = y[5 ln(sint) + 5t cot t] = (sin t)^5t[ 5 ln(sint) + 5t cot t]

Answer 2

y = sin^5t(t)

 

If you mean dy/dt

dy/dt = 5(sin^5t(t))(tcot(t)) + log(sin(t))

 

If you mean dy/dx

dy/dx = 5(sin^5t(t))(tcot(t))(dt/dx) + log(sin(t))(dt/dx)

Answer 3

Do you mean dy/dt because your equation has no x in it.