derivative of-7x^2+400x

{ "query": { "display": "$$\\frac{d}{dx}\\left(-7x^{2}+400x\\right)$$", "symbolab_question": "DERIVATIVE#\\frac{d}{dx}(-7x^{2}+400x)" }, "solution": { "level": "PERFORMED", "subject": "Calculus", "topic": "Derivatives", "subTopic": "Derivatives", "default": "-14x+400", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{d}{dx}\\left(-7x^{2}+400x\\right)=-14x+400$$", "input": "\\frac{d}{dx}\\left(-7x^{2}+400x\\right)", "steps": [ { "type": "step", "primary": "Apply the Sum/Difference Rule: $$\\left(f{\\pm}g\\right)'=f'{\\pm}g'$$", "result": "=-\\frac{d}{dx}\\left(7x^{2}\\right)+\\frac{d}{dx}\\left(400x\\right)" }, { "type": "interim", "title": "$$\\frac{d}{dx}\\left(7x^{2}\\right)=14x$$", "input": "\\frac{d}{dx}\\left(7x^{2}\\right)", "steps": [ { "type": "step", "primary": "Take the constant out: $$\\left(a{\\cdot}f\\right)'=a{\\cdot}f'$$", "result": "=7\\frac{d}{dx}\\left(x^{2}\\right)" }, { "type": "step", "primary": "Apply the Power Rule: $$\\frac{d}{dx}\\left(x^a\\right)=a{\\cdot}x^{a-1}$$", "result": "=7\\cdot\\:2x^{2-1}", "meta": { "practiceLink": "/practice/derivatives-practice#area=main&subtopic=Power%20Rule", "practiceTopic": "Power Rule" } }, { "type": "step", "primary": "Simplify", "result": "=14x", "meta": { "solvingClass": "Solver" } } ], "meta": { "solvingClass": "Derivatives", "interimType": "Derivatives", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYpQtxQSQCpdcnbP/kguSL26TdaV09PMxEKZ9FieghTFwpmYbSDMZJDXIv5YBmTWQJGRLd2VwIqlBNByF6663syQU/sAhO7x3xNQNAStXXN0gsN8HRDsF05vJbrWGdZIqcQ==" } }, { "type": "interim", "title": "$$\\frac{d}{dx}\\left(400x\\right)=400$$", "input": "\\frac{d}{dx}\\left(400x\\right)", "steps": [ { "type": "step", "primary": "Take the constant out: $$\\left(a{\\cdot}f\\right)'=a{\\cdot}f'$$", "result": "=400\\frac{dx}{dx}" }, { "type": "step", "primary": "Apply the common derivative: $$\\frac{dx}{dx}=1$$", "result": "=400\\cdot\\:1" }, { "type": "step", "primary": "Simplify", "result": "=400", "meta": { "solvingClass": "Solver" } } ], "meta": { "solvingClass": "Derivatives", "interimType": "Derivatives", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYjAy2+gf9owd1PvbPR2xs6ecWM5XpXh7YOsEqpbUSEW7p4lfpY4MaOqUL7RZf1bUgEeCBKuYKgaNJ253gLI69U6wC8162KxXnBSuryy0l2Q3Vu5d9LmQembR42SDoOntsA==" } }, { "type": "step", "result": "=-14x+400" } ], "meta": { "solvingClass": "Derivatives", "practiceLink": "/practice/derivatives-practice", "practiceTopic": "Derivatives" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "y=-14x+400" }, "showViewLarger": true } }, "meta": { "showVerify": true } }