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    <p>Here an example:</p> <pre><code>&gt; library(Ryacas) &gt; s &lt;- Sym("s") &gt; nu &lt;- Sym("nu") &gt; theta &lt;- Sym("theta") &gt; e &lt;- exp((nu / (theta * (1 - nu))) * (1 - (1 + theta * s / nu)^(1 - nu))) &gt; de &lt;- deriv(e, s) &gt; de expression(-(exp((1 - (theta * s/nu + 1)^(1 - nu)) * nu/(theta * (1 - nu))) * (theta * (1 - nu) * (nu * ((theta * s/nu + 1)^(1 - nu - 1) * ((1 - nu) * (nu * theta)))))/nu^2)/(theta * (1 - nu))^2) &gt; Simplify(de) expression(-(exp((1 - (theta * s/nu + 1)^(1 - nu)) * nu/(theta * (1 - nu))) * (theta * s/nu + 1)^(1 - nu - 1))) </code></pre> <p>Note that we did get some simplification but the simplification was not perfect since the <code>1 - nu - 1</code> at the end could have been further simplified but was not.</p> <p>Here is an example of repeated derivatives (however, you will likely run into trouble if you really need to take this as high as 10):</p> <pre><code>&gt; de &lt;- e &gt; for(i in 1:3) print(de &lt;- Simplify(deriv(de, s))) expression(-(exp((1 - (theta * s/nu + 1)^(1 - nu)) * nu/(theta * (1 - nu))) * (theta * s/nu + 1)^(1 - nu - 1))) expression((((theta * s/nu + 1)^(1 - nu - 1))^2 * exp((1 - (theta * s/nu + 1)^(1 - nu)) * nu/(theta * (1 - nu))) * nu^2 + exp((1 - (theta * s/nu + 1)^(1 - nu)) * nu/(theta * (1 - nu))) * theta * nu^2 * (theta * s/nu + 1)^(1 - nu - 1 - 1))/nu^2) expression((-3 * (nu * (theta * s/nu + 1)^(1 - nu - 1) * (theta * s/nu + 1)^(1 - nu - 1 - 1) * theta) - nu * ((theta * s/nu + 1)^(1 - nu - 1))^3 - nu * theta^2 * (theta * s/nu + 1)^(1 - nu - 1 - 1 - 1) - theta^2 * (theta * s/nu + 1)^(1 - nu - 1 - 1 - 1)) * exp((1 - (theta * s/nu + 1)^(1 - nu)) * nu/(theta * (1 - nu)))/nu) </code></pre> <p>Added:</p> <p>If the intermediate results are not needed one can do this to get the second derivative but again its unlikely it will handle a 10th derivative:</p> <pre><code>&gt; Simplify(deriv(e, s, 2)) expression(exp((1 - (theta * s/nu + 1)^(1 - nu)) * nu/(theta * (1 - nu))) * (theta * (theta * s/nu + 1)^(1 - nu - 1 - 1) + ((theta * s/nu + 1)^(1 - nu - 1))^2)) </code></pre>
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    1. POSymbolic derivatives and simplification in R
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    1. COThank you ! This is basically what I did. However, as you pointed out, the simplification is not perfect and I have some difficulties to compute derivatives of higher order.
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    2. COAn example of repeated derivatives has been added but as noted it will likely run into trouble if you try to take sufficiently high ones.
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    3. COThank you for the job you made. I have upgraded your answer.
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