ex04_solutions_1.html

Solutions

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$(*2*)D[x^4 + 3x - Sin[x], {x, 2}]$

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$(*3*)x[t_] = 40 - 5t - 5t^2 ; v[t_] = D[x[t], t] ; a[t_] = D[x[t], {t, 2}] ; x[2] v[2] a[2]$

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(*4*)Plot[{v[t], a[t]}, {t, 0, 4}, PlotStyle {Dashing[{0.01}], Dashing[{}]}]

[Graphics:../HTMLFiles/ex04_solutions_22.gif]

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The function Together pulls the terms of a sum over a common denominator.

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(*5*)Clear[f, g] D[f[g[x]], x] D[f[x] g[x], x] D[f[x]/g[x], x]//Together

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Note the syntax for D: When writing D[f[x,y],x,y], the last variable in the list (here y), is the one with respect to which the derivative is calculated first.

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$(*6*)f[x_, y_] = x^3 y^4D[f[x, y], x] D[f[x, y], y] D[f[x, y], {x, 2}] D[f[x, y], {y, 2}] D[f[x, y], x, y] D[f[x, y], y, x, y]$

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Created by Mathematica (April 10, 2007)