求解一道英文微积分问题 急急急~~

求解一道英文微积分问题 急急急~~
A particle is moving along the curve y=2(4x+5)^(1/2). As the particle passes through the point (5,10), its x-coordinate increases at a rate of 4 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
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jhyuan88 幼苗

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质点与原点距离 s=(x^2+y^2)^(1/2)=(x^2+4(4x+5))^(1/2)
ds/dt(x=5)=(ds/dx)*(dx/dt)(x=5)=[(x+8)/(x^2+4(4x+5))^(1/2)]*(dx/dt)=52/5*sqr5

1年前

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