Find the Derivative - d/dt sin(t)^2

Problem

d(sin(t))/d(t)

Solution

1. Identify the outer and inner functions to apply the Power Rule and the Chain Rule.

2. Apply the Power Rule to the outer function, which is the square of the sine function.

d(sin(t))/d(t)=2*sin(t)⋅d(sin(t))/d(t)

3. Differentiate the inner function, sin(t) with respect to t

d(sin(t))/d(t)=cos(t)

4. Substitute the derivative of the inner function back into the expression.

2*sin(t)*cos(t)

5. Simplify the expression using the double angle identity for sine, where sin(2*t)=2*sin(t)*cos(t)

sin(2*t)

Final Answer

d(sin(t))/d(t)=sin(2*t)

Want more problems? Check here!