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Audrey
Audrey asked in Science & MathematicsMathematics · 5 years ago

Parametric Eqns!?

x = ln(5t)

y = e^(5t)

find dy/dx and d^2y/dx^2

2 Answers

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  • Como
    Lv 7
    5 years ago

    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
    Lv 5
    5 years ago

    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

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