How this calculation works
Calculate the second derivative of y with respect to x from time derivatives.
THE FORMULA
d²y/dx²=(x′y″−y′x″)/(x′)³A worked example
x′=2, y′=6, x″=0, y″=2 give 4/8=0.5.
Good to know
The derivative dx/dt must be nonzero.
Reference: OpenStax Calculus Volume 3 (opens in a new tab) ↗
Read the result
Calculate the second derivative of y with respect to x from time derivatives.
The primary result is labeled “Second derivative”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The derivative dx/dt must be nonzero.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
x′=2, y′=6, x″=0, y″=2 give 4/8=0.5.
Which rule does this calculator apply?
d²y/dx²=(x′y″−y′x″)/(x′)³