$$ \begin{aligned} f(x) & = \, x \, \\[2 em] f\prime(x) &= {{\left(\left(3\,a\,\sin \left(3\,x\right)-5\,a\right)\,\cos \left( 5\,x^4\right)+a\,3^{x+1}\,\sin \left(3\,x\right)-5\,a\,3^{x}\right) \,\left(\sec \left(\cos \left(3\,x\right)+5\,x\right)\right)^2\, \left(\ln \left(\cos \left(5\,x^4\right)+3^{x}\right)\right)^2+ \left(\left(x^{x}\,\ln x+x^{x}\right)\,\cos \left(5\,x^4\right)+x^{ x}\,3^{x}\,\ln x+x^{x}\,3^{x}\right)\,\ln \left(\cos \left(5\,x^4 \right)+3^{x}\right)+20\,x^{x+3}\,\sin \left(5\,x^4\right)-\ln 3\,x ^{x}\,3^{x}}\over{2\,\left(\cos \left(5\,x^4\right)+3^{x}\right)\, \left(\ln \left(\cos \left(5\,x^4\right)+3^{x}\right)\right)^2\, \sqrt{-{{a\,\tan \left(\cos \left(3\,x\right)+5\,x\right)\,\ln \left(\cos \left(5\,x^4\right)+3^{x}\right)-x^{x}}\over{\ln \left( \cos \left(5\,x^4\right)+3^{x}\right)}}}}} \end{aligned} $$

Derivative Calculator