Derivative rules Let u ( t ) = 2 t 3 i + ( t 2 − 1 ) j − 8 k a n d v ( t ) = e t i + 2 e − t j − e 2 t k . Compute the derivative of the following functions. 33. u ( t 4 − 2 t )
Derivative rules Let u ( t ) = 2 t 3 i + ( t 2 − 1 ) j − 8 k a n d v ( t ) = e t i + 2 e − t j − e 2 t k . Compute the derivative of the following functions. 33. u ( t 4 − 2 t )
Solution Summary: The author explains how to compute the derivative of the vector-valued function u(t4-2).
Air is being pumped into a spherical weather balloon. Atany time t , the volume of the balloon is V(t) and its radiusis r(t).(a) What do the derivatives dV/dr and dV/dt represent?(b) Express dV/dt in terms of dr/dt .
find the partial derivative of the function with respectto each variable. P(n, R, T, V ) = nRT/V (the ideal gas law)
Consider a particle moving along the x-axis, where x(t) is the position of the particle at time t, x′(t) is its velocity, and x″(t) is its acceleration. A particle moves along the x-axis at a velocity of v(t) = 1/√t, t > 0. At time t = 1, its position is x = 4. Find the acceleration and position functions for the particle.
Chapter 14 Solutions
Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
University Calculus: Early Transcendentals (4th Edition)
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY