derivative of tan(pi/4)

{ "query": { "display": "$$\\frac{d}{dx}\\left(\\tan\\left(\\frac{π}{4}\\right)\\right)$$", "symbolab_question": "DERIVATIVE#\\frac{d}{dx}(\\tan(\\frac{π}{4}))" }, "solution": { "level": "PERFORMED", "subject": "Calculus", "topic": "Derivatives", "subTopic": "Derivatives", "default": "0", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{d}{dx}\\left(\\tan\\left(\\frac{π}{4}\\right)\\right)=0$$", "input": "\\frac{d}{dx}\\left(\\tan\\left(\\frac{π}{4}\\right)\\right)", "steps": [ { "type": "interim", "title": "$$\\tan\\left(\\frac{π}{4}\\right)=1$$", "input": "\\tan\\left(\\frac{π}{4}\\right)", "steps": [ { "type": "step", "primary": "Use the following trivial identity:$${\\quad}\\tan\\left(\\frac{π}{4}\\right)=1$$", "secondary": [ "$$\\tan\\left(x\\right)$$ periodicity table with $$πn$$ cycle:<br/>$$\\begin{array}{|c|c|}\\hline x&\\tan(x)\\\\\\hline 0&0\\\\\\hline \\frac{π}{6}&\\frac{\\sqrt{3}}{3}\\\\\\hline \\frac{π}{4}&1\\\\\\hline \\frac{π}{3}&\\sqrt{3}\\\\\\hline \\frac{π}{2}&\\pm\\infty\\\\\\hline \\frac{2π}{3}&-\\sqrt{3}\\\\\\hline \\frac{3π}{4}&-1\\\\\\hline \\frac{5π}{6}&-\\frac{\\sqrt{3}}{3}\\\\\\hline &\\\\\\hline \\end{array}$$" ], "result": "=1" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7+AlE1DWLUO8NM1UnpPTc/MRWF7N9UkpRzvD4vYPAPuWrju+5Z51e/ZZSD3gRHwjBE9/03SOiEv+BIHutWLr6nQAEekyUOsnZpyOEuLzmz6i4aoXXQxVEoOTEBa/NKcrU" } }, { "type": "step", "result": "=\\frac{d}{dx}\\left(1\\right)" }, { "type": "step", "primary": "Derivative of a constant: $$\\frac{d}{dx}\\left({a}\\right)=0$$", "result": "=0" } ], "meta": { "solvingClass": "Derivatives", "practiceLink": "/practice/derivatives-practice", "practiceTopic": "Derivatives" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "y=0" }, "showViewLarger": true } }, "meta": { "showVerify": true } }