A bead is constrained to move on a wire with the shape of the graph y=arctan(x^3). When the bead is at (1,pi/4), dx/dt = 2. What is dy/dt at this time.
can anyone help how to solve this? im really confused wat to do here
can anyone help how to solve this? im really confused wat to do here
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It's a related rates problem.
dy/dt = (dy/dx)(dx/dt)
Here, y = arctan(x³) so
dy/dx = 1/(1 + (x³)²) * (3x²)
= 3x²/(1 + x^6)
When x = 1, dy/dx = 3/2. (The y-value is not needed in this case.)
You are also given that dx/dt = 2 at this time. Therefore, using the formula above,
dy/dt = (3/2)(2) = 3 at this time.
dy/dt = (dy/dx)(dx/dt)
Here, y = arctan(x³) so
dy/dx = 1/(1 + (x³)²) * (3x²)
= 3x²/(1 + x^6)
When x = 1, dy/dx = 3/2. (The y-value is not needed in this case.)
You are also given that dx/dt = 2 at this time. Therefore, using the formula above,
dy/dt = (3/2)(2) = 3 at this time.