Compute the following derivative ddt 6t2 i squareroot of t

Compute the following derivative d/dt [(6t^2 i + squareroot of t j - 9t^-1 k) middit (cos t+sin 3t j-)]

Solution:

d/dt(u/v)=uv\' +vu^\'

v¹ is first derivative wrt t

and u¹ is first derivative wrt t

here u=6t²i-tj-9t^-1k v=costi+sin3tj-9tk

u^\' =12ti- 1/2tj-9(-1/t²)k v\'=-sinti+3cos3tj-9k

$Compute the following derivative d/dt [(6t^2 i + squareroot of t j - 9t^-1 k) middit (cos t+sin 3t j-)] SolutionSolution: d/dt(u/v)=uv\' +vu\' v1 is first deri$

Compute the following derivative ddt 6t2 i squareroot of t

Solution

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