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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Find dy/dx. x = t / (9 + t) y = √(9 + t).
Solution:
We apply differentiation of parametric functions as x = f(t) and y = g(t)
Let us find dy/dx by finding dy/dt and dx/dt
dy/dx = dy/dt . dt/dx
x = t/(9 + t)
dx/dt = ((9+t)dt/dt - t(d9/dt + dt/dt))/ (9+t)2
= ((9 + t) - t(0 + 1)) / (9+t)2
= 9 + t - t / (9+t)2
= 9/(9+t)2
y = √9+t
dy/dt = (½)(1)1/(√9+t)
= 1/ 2((√9+t))
dy/dx = (dy/dt)/(dx/dt) = 1/(2(√9+t)) / 9/(9+t)2
= (1/18) × ((9 + t)2/ √(9+t))
dy/dx = (1/18)(9 + t)3/2
Find dy/dx. x = t / (9 + t) y = √(9 + t).
Summary:
dy/dx = (1/18)(9 + t)3/2 when x = t / (9 + t)and y = √(9 + t).
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