Question

If y = sint + cost, then second derivative of y w.r.t t is

2 sin t cos t

-(sin t + cos t)


sin t - cos t

cos t - sin t​

Answer 1

Answer:

cost-sint is the second derivate of the given question

Answer 2

Answer:

The solution  is '-(sint+cost)'.

Explanation:

The derivative of a function in mathematics is the rate of change of a function with respect to a variable. In other terms, the derivative is the slope of a line i.e. tangent to the curve at a specific point.

Derivatives are the basic key for doing calculus and differential equations.

1. The 1st derivative of 'Sint' would be 'cost'.
2. The 1st derivative of 'cost' would be '-Sint'.
3. Here the given function is 'y = sint + cost'.
4. So the first derivative of Y with respect to t will be:-

                  $\frac{dy}{dt}= \frac{d(sint+cost)}{dt}\\\frac{dy}{dt}= cost - sint$

    5. The second derivative of Y with respect to t will be:-

                  $\frac{d^2y}{dt^2}= \frac{d(cost-sint)}{dt}\\\frac{d^2y}{dt^2}= -sint-cost = -(sint +cost)$

Hence, the answer to the question is -(sint +cost).