(\partial)/(\partial y)(e^xcos(y))

{ "query": { "display": "$$\\frac{\\partial\\:}{\\partial\\:y}\\left(e^{x}\\cos\\left(y\\right)\\right)$$", "symbolab_question": "DERIVATIVE#\\frac{\\partial }{\\partial y}(e^{x}\\cos(y))" }, "solution": { "level": "PERFORMED", "subject": "Calculus", "topic": "Derivatives", "subTopic": "Partial Derivatives", "default": "-e^{x}\\sin(y)", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{\\partial\\:}{\\partial\\:y}\\left(e^{x}\\cos\\left(y\\right)\\right)=-e^{x}\\sin\\left(y\\right)$$", "input": "\\frac{\\partial\\:}{\\partial\\:y}\\left(e^{x}\\cos\\left(y\\right)\\right)", "steps": [ { "type": "step", "primary": "Treat $$x\\:$$as a constant" }, { "type": "step", "primary": "Take the constant out: $$\\left(a{\\cdot}f\\right)'=a{\\cdot}f'$$", "result": "=e^{x}\\frac{\\partial\\:}{\\partial\\:y}\\left(\\cos\\left(y\\right)\\right)" }, { "type": "step", "primary": "Apply the common derivative: $$\\frac{\\partial\\:}{\\partial\\:y}\\left(\\cos\\left(y\\right)\\right)=-\\sin\\left(y\\right)$$", "result": "=e^{x}\\left(-\\sin\\left(y\\right)\\right)" }, { "type": "step", "primary": "Simplify", "result": "=-e^{x}\\sin\\left(y\\right)", "meta": { "solvingClass": "Solver" } } ], "meta": { "solvingClass": "Derivatives", "practiceLink": "/practice/derivatives-practice#area=main&subtopic=Partial%20Derivatives", "practiceTopic": "Partial Derivatives" } }, "meta": { "showVerify": true } }