{
"query": {
"display": "derivative of $$f\\left(x\\right)=4x+7,\\:\\at\\:x=5$$",
"symbolab_question": "PRE_CALC#derivative f(x)=4x+7,\\at x=5"
},
"solution": {
"level": "PERFORMED",
"subject": "Calculus",
"topic": "Derivatives",
"subTopic": "Derivative at a Point"
},
"steps": {
"type": "interim",
"steps": [
{
"type": "interim",
"title": "$$\\frac{d}{dx}\\left(4x+7\\right)=4$$",
"input": "\\frac{d}{dx}\\left(4x+7\\right)",
"steps": [
{
"type": "step",
"primary": "Apply the Sum/Difference Rule: $$\\left(f{\\pm}g\\right)'=f'{\\pm}g'$$",
"result": "=\\frac{d}{dx}\\left(4x\\right)+\\frac{d}{dx}\\left(7\\right)"
},
{
"type": "interim",
"title": "$$\\frac{d}{dx}\\left(4x\\right)=4$$",
"input": "\\frac{d}{dx}\\left(4x\\right)",
"steps": [
{
"type": "step",
"primary": "Take the constant out: $$\\left(a{\\cdot}f\\right)'=a{\\cdot}f'$$",
"result": "=4\\frac{dx}{dx}"
},
{
"type": "step",
"primary": "Apply the common derivative: $$\\frac{dx}{dx}=1$$",
"result": "=4\\cdot\\:1"
},
{
"type": "step",
"primary": "Simplify",
"result": "=4",
"meta": {
"solvingClass": "Solver"
}
}
],
"meta": {
"solvingClass": "Derivatives",
"interimType": "Derivatives",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYjTQT54ZonDS7voDaGrIxyrZGku9zFkxwe1dTH8vycb9lXydCAnPpeOlbdfKkqvrL1NbbqpyK7JQEZdATEJR51jxWDAE4KteS3Xb/OKFHmJV"
}
},
{
"type": "interim",
"title": "$$\\frac{d}{dx}\\left(7\\right)=0$$",
"input": "\\frac{d}{dx}\\left(7\\right)",
"steps": [
{
"type": "step",
"primary": "Derivative of a constant: $$\\frac{d}{dx}\\left({a}\\right)=0$$",
"result": "=0"
}
],
"meta": {
"solvingClass": "Derivatives",
"interimType": "Derivatives",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYr/PPZDkjJg1JcijqZvGH+JJ8Vk6wvKjVnTtwWT18bQnz7FeFrf3rcM8IZlDz2c0dm5O2bEw0Ql6ne7k1AUriTuldgLTbPmvou0JbfidNFAp"
}
},
{
"type": "step",
"result": "=4+0"
},
{
"type": "step",
"primary": "Simplify",
"result": "=4",
"meta": {
"solvingClass": "Solver"
}
}
],
"meta": {
"solvingClass": "Derivatives",
"interimType": "Derivatives"
}
},
{
"type": "interim",
"title": "Find the value of $$4$$ for $$=5$$",
"steps": [
{
"type": "step",
"primary": "Plug $$=5$$ into the equation $$4$$"
},
{
"type": "interim",
"title": "Simplify :$${\\quad}$$",
"meta": {
"interimType": "Generic Simplify Specific 1Eq"
}
}
],
"meta": {
"interimType": "Value At Point Top 2Eq"
}
}
],
"meta": {
"solvingClass": "PreCalc"
}
}
}
Solution
derivative of
Solution
Solution steps
Find the value of for