15–48. Derivatives Find the derivative of the following functions.
y = In (x³+1)^π

Deriving trigonometric identities

a. Differentiate both sides of the identity cos 2t = cos² t−sin² t to prove that sin 2 t= 2 sin t cos t.

Deriving trigonometric identities

b. Verify that you obtain the same identity for sin2t as in part (a) if you differentiate the identity cos 2t = 2 cos² t−1.

Deriving trigonometric identities

c. Differentiate both sides of the identity sin 2t = 2 sin t cost to prove that cos 2t = cos²t−sin²t.

{Use of Tech} Cell population The population of a culture of cells after t days is approximated by the function P(t)=1600 / 1 + 7e^−0.02t, for t≥0.

e. Graph the growth rate. When is it a maximum and what is the population at the time that the growth rate is a maximum? 

15–48. Derivatives Find the derivative of the following functions.

y = 5^3t

15–48. Derivatives Find the derivative of the following functions.

y = 10^In 2x

9–61. Evaluate and simplify y'.

y = e^2θ

9–61. Evaluate and simplify y'.

y = e^sin x+2x+1