There are 2 questions in this calculation: for each question, the 2 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/2]Find\ the\ second\ derivative\ of\ function\ sech(xx + 5x)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sech(x^{2} + 5x)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( sech(x^{2} + 5x)\right)}{dx}\\=&-sech(x^{2} + 5x)tanh(x^{2} + 5x)(2x + 5)\\=&-2xtanh(x^{2} + 5x)sech(x^{2} + 5x) - 5tanh(x^{2} + 5x)sech(x^{2} + 5x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -2xtanh(x^{2} + 5x)sech(x^{2} + 5x) - 5tanh(x^{2} + 5x)sech(x^{2} + 5x)\right)}{dx}\\=&-2tanh(x^{2} + 5x)sech(x^{2} + 5x) - 2xsech^{2}(x^{2} + 5x)(2x + 5)sech(x^{2} + 5x) - 2xtanh(x^{2} + 5x)*-sech(x^{2} + 5x)tanh(x^{2} + 5x)(2x + 5) - 5sech^{2}(x^{2} + 5x)(2x + 5)sech(x^{2} + 5x) - 5tanh(x^{2} + 5x)*-sech(x^{2} + 5x)tanh(x^{2} + 5x)(2x + 5)\\=&-2tanh(x^{2} + 5x)sech(x^{2} + 5x) - 4x^{2}sech^{3}(x^{2} + 5x) - 20xsech^{3}(x^{2} + 5x) + 4x^{2}tanh^{2}(x^{2} + 5x)sech(x^{2} + 5x) + 20xtanh^{2}(x^{2} + 5x)sech(x^{2} + 5x) - 25sech^{3}(x^{2} + 5x) + 25tanh^{2}(x^{2} + 5x)sech(x^{2} + 5x)\\ \end{split}\end{equation} \]\[ \begin{equation}\begin{split}[2/2]Find\ the\ second\ derivative\ of\ function\ csch(xx + 5x)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = csch(x^{2} + 5x)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( csch(x^{2} + 5x)\right)}{dx}\\=&-csch(x^{2} + 5x)coth(x^{2} + 5x)(2x + 5)\\=&-2xcoth(x^{2} + 5x)csch(x^{2} + 5x) - 5coth(x^{2} + 5x)csch(x^{2} + 5x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -2xcoth(x^{2} + 5x)csch(x^{2} + 5x) - 5coth(x^{2} + 5x)csch(x^{2} + 5x)\right)}{dx}\\=&-2coth(x^{2} + 5x)csch(x^{2} + 5x) - 2x*-csch^{2}(x^{2} + 5x)(2x + 5)csch(x^{2} + 5x) - 2xcoth(x^{2} + 5x)*-csch(x^{2} + 5x)coth(x^{2} + 5x)(2x + 5) - 5*-csch^{2}(x^{2} + 5x)(2x + 5)csch(x^{2} + 5x) - 5coth(x^{2} + 5x)*-csch(x^{2} + 5x)coth(x^{2} + 5x)(2x + 5)\\=&-2coth(x^{2} + 5x)csch(x^{2} + 5x) + 4x^{2}csch^{3}(x^{2} + 5x) + 20xcsch^{3}(x^{2} + 5x) + 4x^{2}coth^{2}(x^{2} + 5x)csch(x^{2} + 5x) + 20xcoth^{2}(x^{2} + 5x)csch(x^{2} + 5x) + 25csch^{3}(x^{2} + 5x) + 25coth^{2}(x^{2} + 5x)csch(x^{2} + 5x)\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!