find dirivitive of T(t)

**icelated** · June 14th 2012, 06:56 PM

let $\vec T(t) = \frac{1}{\sqrt{10+ 4t^2}} ( 3 \hat i - \hat j + 2t \hat k) find \frac {d \vec T}{dt}$

I am not sure how to do this.

**richard1234** · June 14th 2012, 11:28 PM

Note that

$\frac{d}{dt} \frac{1}{\sqrt{10 + 4t^2}} = -4t (10+4t^2)^{-\frac{3}{2}}$ , and

$\frac{d}{dt} \frac{2t}{\sqrt{10 + 4t^2}} = \frac{2 \sqrt{10 + 4t^2} - t(10 + 4t^2)^{-\frac{1}{2}}}{10 + 4t^2}$ (applying the chain and quotient rules)

$\frac{d \vec{T}}{dt}$ is computed by taking the derivatives of each of vector T's components, i.e.

$\frac{d \vec{T}}{dt} = \frac{d}{dt} \frac{3}{\sqrt{10 + 4t^2}}\vec{i} - \frac{d}{dt} \frac{1}{\sqrt{10 + 4t^2}} \vec{j} + \frac{d}{dt} \frac{2t}{\sqrt{10 + 4t^2}} \vec{j}$

Use the given derivatives and substitute.

Thread: find dirivitive of T(t)

LinkBack

Thread Tools

Display

find dirivitive of T(t)

Re: find dirivitive of T(t)

Similar Math Help Forum Discussions

Find an Equation of the Tangent Line to the parabola at the given point and find....

Given 3 points, find the area of the triangle/find the volume of the parallelepiped

How to find the find local max, min and inflection points from an integral?

Find condition that wedge may move and if it does, find acceleration?

Dirivitive using the power "e"

Search Tags