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Math Help - Differentiation

  1. #1
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    Differentiation

    Find dy/dx in terms of x if x = t^sqrt(t) , y = e^t

    also, dy/dx in terms of theta if x = sin^3 4(theta) , y = cos^3 4(theta)

    Thanks!
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  2. #2
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    Quote Originally Posted by ose90 View Post
    Find dy/dx in terms of x if x = t^sqrt(t) , y = e^t
    Find:

    \frac{\mathrm{d}x}{\mathrm{d}t} Using chain rule and product rule.

    And \frac{\mathrm{d}y}{\mathrm{d}t} Using standard differentiation e.g. \frac{\mathrm{d}(e^x)}{\mathrm{d}x} = e^x.

    Then:

    \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{\mathrm{d}y}{\mathrm{d}t} \times \frac{\mathrm{d}t}{\mathrm{d}x}

    Quote Originally Posted by ose90 View Post
    also, dy/dx in terms of theta if x = sin^3 4(theta) , y = cos^3 4(theta)

    Thanks!
    Find:

    \frac{\mathrm{d}x}{\mathrm{d}\theta} Using chain rule.

    And \frac{\mathrm{d}y}{\mathrm{d}\theta} Using chain rule.

    Then:

    \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{\mathrm{d}y}{\mathrm{d}\theta} \times \frac{\mathrm{d}\theta}{\mathrm{d}x}
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