Parametric Eqns!?
x = ln(5t)
y = e^(5t)
find dy/dx and d^2y/dx^2
x = ln(5t)
y = e^(5t)
find dy/dx and d^2y/dx^2
Como
dx / dt = 1 / t
dy / dt = 5 e^(5t)
dy / dx = 5t e^(5t)
d²y / dx² = d/dt [ 5t e^(5t) ] dt/dx
d²y / dx² = [ 5 e^(5t) + 25 t e^(5t) ] t
d²y / dx² = 5 e^(5t) [ 1 + 5 t ] t
d²y / dx² = 5 t e^(5t) [ 1 + 5t ]
Xenyak
y = e⁵ᵗ
dy/dt = 5e⁵ᵗ
x = ln(5t)
dx/dt = 1 / t
By chain rule:
dy/dx = dy/dt ÷ dx/dt
dy/dx = 5e⁵ᵗ ÷ 1 / t
dy/dx = 5te⁵ᵗ
Same can be done for d²y/dx²