derivative of 3x^2-6x

{ "query": { "display": "$$\\frac{d}{dx}\\left(3x^{2}-6x\\right)$$", "symbolab_question": "DERIVATIVE#\\frac{d}{dx}(3x^{2}-6x)" }, "solution": { "level": "PERFORMED", "subject": "Calculus", "topic": "Derivatives", "subTopic": "Derivatives", "default": "6x-6", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{d}{dx}\\left(3x^{2}-6x\\right)=6x-6$$", "input": "\\frac{d}{dx}\\left(3x^{2}-6x\\right)", "steps": [ { "type": "step", "primary": "Apply the Sum/Difference Rule: $$\\left(f{\\pm}g\\right)'=f'{\\pm}g'$$", "result": "=\\frac{d}{dx}\\left(3x^{2}\\right)-\\frac{d}{dx}\\left(6x\\right)" }, { "type": "interim", "title": "$$\\frac{d}{dx}\\left(3x^{2}\\right)=6x$$", "input": "\\frac{d}{dx}\\left(3x^{2}\\right)", "steps": [ { "type": "step", "primary": "Take the constant out: $$\\left(a{\\cdot}f\\right)'=a{\\cdot}f'$$", "result": "=3\\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": "=3\\cdot\\:2x^{2-1}", "meta": { "practiceLink": "/practice/derivatives-practice#area=main&subtopic=Power%20Rule", "practiceTopic": "Power Rule" } }, { "type": "step", "primary": "Simplify", "result": "=6x", "meta": { "solvingClass": "Solver" } } ], "meta": { "solvingClass": "Derivatives", "interimType": "Derivatives", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYoMCvILd9ATo1x5jS/pE9/WTdaV09PMxEKZ9FieghTFwhVeofZ6TN6CjAjiGv3Kp4KN6Hv6MoTMtvtU0IQwXdn+0Pe4MM1RA6/7KiCIasGeudcfHQ5Gx5B84odmIQ8SsiA==" } }, { "type": "interim", "title": "$$\\frac{d}{dx}\\left(6x\\right)=6$$", "input": "\\frac{d}{dx}\\left(6x\\right)", "steps": [ { "type": "step", "primary": "Take the constant out: $$\\left(a{\\cdot}f\\right)'=a{\\cdot}f'$$", "result": "=6\\frac{dx}{dx}" }, { "type": "step", "primary": "Apply the common derivative: $$\\frac{dx}{dx}=1$$", "result": "=6\\cdot\\:1" }, { "type": "step", "primary": "Simplify", "result": "=6", "meta": { "solvingClass": "Solver" } } ], "meta": { "solvingClass": "Derivatives", "interimType": "Derivatives", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYhppyBxBdApfk+SBOUguWFnZGku9zFkxwe1dTH8vycb9iU7QbEXaQW7Sg4nSYYaTV1NbbqpyK7JQEZdATEJR51hjHS9CfrzgF/gRWKQsm38l" } }, { "type": "step", "result": "=6x-6" } ], "meta": { "solvingClass": "Derivatives", "practiceLink": "/practice/derivatives-practice", "practiceTopic": "Derivatives" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "y=6x-6" }, "showViewLarger": true } }, "meta": { "showVerify": true } }