{"generator":"equations.calculus","version":1,"value":{"problems":[{"prompt":"d\/dx [ (5x - 6)sin(x) ]","prompt_latex":"\\frac{d}{dx}\\left[\\, \\left(5x - 6\\right)\\sin\\left(x\\right) \\,\\right]","answer":"5sin(x) + (5x - 6)cos(x)","answer_latex":"5\\sin\\left(x\\right) + \\left(5x - 6\\right)\\cos\\left(x\\right)","rule":"product"},{"prompt":"d\/dx [ 6x^2 + 4x - 6 ]","prompt_latex":"\\frac{d}{dx}\\left[\\, 6x^{2} + 4x - 6 \\,\\right]","answer":"12x + 4","answer_latex":"12x + 4","rule":"power"},{"prompt":"d\/dx [ 5exp(x) - 6x^2 ]","prompt_latex":"\\frac{d}{dx}\\left[\\, 5e^{x} - 6x^{2} \\,\\right]","answer":"5exp(x) - 12x","answer_latex":"5e^{x} - 12x","rule":"exp_log"},{"prompt":"d\/dx [ x^3*sin(x) ]","prompt_latex":"\\frac{d}{dx}\\left[\\, x^{3} \\cdot \\sin\\left(x\\right) \\,\\right]","answer":"3x^2sin(x) + x^3*cos(x)","answer_latex":"3x^{2}\\sin\\left(x\\right) + x^{3} \\cdot \\cos\\left(x\\right)","rule":"product"},{"prompt":"d\/dx [ 2x^2 + 5x ]","prompt_latex":"\\frac{d}{dx}\\left[\\, 2x^{2} + 5x \\,\\right]","answer":"4x + 5","answer_latex":"4x + 5","rule":"power"},{"prompt":"d\/dx [ -2sin(x) - 5x ]","prompt_latex":"\\frac{d}{dx}\\left[\\, -2\\sin\\left(x\\right) - 5x \\,\\right]","answer":"-2cos(x) - 5","answer_latex":"-2\\cos\\left(x\\right) - 5","rule":"trig"}],"count":6},"display":"1. d\/dx [ (5x - 6)sin(x) ]   \u2192   5sin(x) + (5x - 6)cos(x)\n2. d\/dx [ 6x^2 + 4x - 6 ]   \u2192   12x + 4\n3. d\/dx [ 5exp(x) - 6x^2 ]   \u2192   5exp(x) - 12x\n4. d\/dx [ x^3*sin(x) ]   \u2192   3x^2sin(x) + x^3*cos(x)\n5. d\/dx [ 2x^2 + 5x ]   \u2192   4x + 5\n6. d\/dx [ -2sin(x) - 5x ]   \u2192   -2cos(x) - 5","meta":{"latex":[["\\frac{d}{dx}\\left[\\, \\left(5x - 6\\right)\\sin\\left(x\\right) \\,\\right]","5\\sin\\left(x\\right) + \\left(5x - 6\\right)\\cos\\left(x\\right)"],["\\frac{d}{dx}\\left[\\, 6x^{2} + 4x - 6 \\,\\right]","12x + 4"],["\\frac{d}{dx}\\left[\\, 5e^{x} - 6x^{2} \\,\\right]","5e^{x} - 12x"],["\\frac{d}{dx}\\left[\\, x^{3} \\cdot \\sin\\left(x\\right) \\,\\right]","3x^{2}\\sin\\left(x\\right) + x^{3} \\cdot \\cos\\left(x\\right)"],["\\frac{d}{dx}\\left[\\, 2x^{2} + 5x \\,\\right]","4x + 5"],["\\frac{d}{dx}\\left[\\, -2\\sin\\left(x\\right) - 5x \\,\\right]","-2\\cos\\left(x\\right) - 5"]],"problems":6,"stream_bytes_used":31,"rejections":4,"entropy_in_bytes":16,"duration_us":1007},"receipt":{"source":"iss","source_label":"ISS Position","class":"C","class_label":"Observational","caveat":"Carries only tens of bits of genuine surprise. Always mixed with the OS CSPRNG.","narrative":"The ISS was over 42.19\u00b0 S, 162.08\u00b0 W \u2014 2,070 km south-east of Auckland \u2014 when this was drawn.","proof_url":"https:\/\/www.openstreetmap.org\/#map=3\/-42.19\/-162.08","reference":"1793228864","observed_at":"2026-10-28T23:07:44+00:00","degraded":false,"mixed_with_csprng":true,"latency_ms":152,"cached":false},"seed":{"token":"YBJT685884BJAEJ4K1YDVP4QSM","permalink":"https:\/\/randomly.cluxnei.dev\/r\/YBJT685884BJAEJ4K1YDVP4QSM?g=equations.calculus&v=1&p=eyJjb3VudCI6NiwibW9kZSI6ImRlcml2YXRpdmUiLCJydWxlIjoibWl4ZWQifQ&s=iss&r=1793228864"},"uses_entropy":true,"reproducible":true}