General Calculus

Let θ (in radians) be an acute angle in a right triangle and let x and y, respectively, be the lengths of the sides adjacent to and opposite θ. Suppose also that x and y vary with time.
At a certain instant x=7 units and is increasing at 3 unit/s, while y=1 and is decreasing at 18 units/s.
How fast is θ changing at that instant?

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  1. The equation is supposedly

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  2. you know that
    tanθ = y/x
    sec^2θ dθ/dt = (x dy/dt - y dx/dt)/x^2
    so just plug in your numbers.

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  3. if that confuses you, just recall the quotient rule for derivatives, and implicit differentiation.

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