Question

Find d²y/dx²: x(t) = sin t, y(t) = cos t.

Answer 1

To find d²y/dx², we need to differentiate the given y(t) twice with respect to x. The second derivative is (-sin(asin(x)) * (-sin(x))^2) + (-cos(asin(x)) * cos(x)).

Step-by-step explanation:

To find d²y/dx², we need to differentiate the given y(t) function twice with respect to x. Since x(t) = sin(t), we can express y(t) in terms of x: y(t) = cos(t) = cos(asin(x)).

Now, we differentiate y(t) with respect to x twice using the chain rule. The first derivative is -sin(asin(x)) * (cos(x)). The second derivative is (-sin(asin(x)) * (-sin(x))^2) + (-cos(asin(x)) * cos(x)).

Therefore, d²y/dx² = (-sin(asin(x)) * (-sin(x))^2) + (-cos(asin(x)) * cos(x)).