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

Problem

d()/d(t)*t2*sin(t)

Solution

1. Identify the rule needed for the derivative. Since the expression is a product of two functions, t2 and sin(t) use the product rule: (d(u)*v)/d(t)=ud(v)/d(t)+vd(u)/d(t)

2. Assign the functions for the product rule. Let u=t2 and v=sin(t)

3. Differentiate each part individually. The derivative of u is d(t2)/d(t)=2*t The derivative of v is d(sin(t))/d(t)=cos(t)

4. Apply the product rule formula by substituting the functions and their derivatives.

t2d(sin(t))/d(t)+sin(t)d(t2)/d(t)

5. Substitute the calculated derivatives into the expression.

t2*cos(t)+sin(t)*(2*t)

6. Simplify the expression by rearranging the terms.

t2*cos(t)+2*t*sin(t)

Final Answer

(d(t2)*sin(t))/d(t)=t2*cos(t)+2*t*sin(t)

Want more problems? Check here!