Difference between Gradient, Rate of Change and Derivative (Single Variable Calculus)
I was just wondering what the differences between gradient, rate of change and derivative are in terms of single variable calculus. As in can we use “gradient", “rate of change” and "derivative" interchangeably when talking about a function? Thanks in advance.
calculus derivatives
asked Nov 25 at 7:36
J. Smith
241
add a comment |
I was just wondering what the differences between gradient, rate of change and derivative are in terms of single variable calculus. As in can we use “gradient", “rate of change” and "derivative" interchangeably when talking about a function? Thanks in advance.
calculus derivatives
asked Nov 25 at 7:36
J. Smith
241
add a comment |
I was just wondering what the differences between gradient, rate of change and derivative are in terms of single variable calculus. As in can we use “gradient", “rate of change” and "derivative" interchangeably when talking about a function? Thanks in advance.
calculus derivatives
asked Nov 25 at 7:36
J. Smith
241
I was just wondering what the differences between gradient, rate of change and derivative are in terms of single variable calculus. As in can we use “gradient", “rate of change” and "derivative" interchangeably when talking about a function? Thanks in advance.
calculus derivatives
calculus derivatives
asked Nov 25 at 7:36
J. Smith
241
asked Nov 25 at 7:36
J. Smith
241
asked Nov 25 at 7:36
J. Smith
241
asked Nov 25 at 7:36
J. Smith
241
asked Nov 25 at 7:36
J. Smith
241
241
add a comment |
add a comment |
1 Answer
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There are differences in meaning. "Derivative" is the broadest term. It's a certain limit. "Rate of change" is more specialized. It's the derivative with respect to time. I've never heard "gradient" used with a single-variable function, but I suppose it's technically correct. But it's still a more narrow term than "derivative", because functions $f:mathbb{R}^n to mathbb{R}^m,$ with $m>1$, have derivatives but not gradients.
I think using gradient in single variable calculus would just be confusing.
answered Nov 25 at 13:43
B. Goddard
18.3k21340
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
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oldest
votes
There are differences in meaning. "Derivative" is the broadest term. It's a certain limit. "Rate of change" is more specialized. It's the derivative with respect to time. I've never heard "gradient" used with a single-variable function, but I suppose it's technically correct. But it's still a more narrow term than "derivative", because functions $f:mathbb{R}^n to mathbb{R}^m,$ with $m>1$, have derivatives but not gradients.
I think using gradient in single variable calculus would just be confusing.
answered Nov 25 at 13:43
B. Goddard
18.3k21340
add a comment |
There are differences in meaning. "Derivative" is the broadest term. It's a certain limit. "Rate of change" is more specialized. It's the derivative with respect to time. I've never heard "gradient" used with a single-variable function, but I suppose it's technically correct. But it's still a more narrow term than "derivative", because functions $f:mathbb{R}^n to mathbb{R}^m,$ with $m>1$, have derivatives but not gradients.
I think using gradient in single variable calculus would just be confusing.
answered Nov 25 at 13:43
B. Goddard
18.3k21340
add a comment |
There are differences in meaning. "Derivative" is the broadest term. It's a certain limit. "Rate of change" is more specialized. It's the derivative with respect to time. I've never heard "gradient" used with a single-variable function, but I suppose it's technically correct. But it's still a more narrow term than "derivative", because functions $f:mathbb{R}^n to mathbb{R}^m,$ with $m>1$, have derivatives but not gradients.
I think using gradient in single variable calculus would just be confusing.
answered Nov 25 at 13:43
B. Goddard
18.3k21340
There are differences in meaning. "Derivative" is the broadest term. It's a certain limit. "Rate of change" is more specialized. It's the derivative with respect to time. I've never heard "gradient" used with a single-variable function, but I suppose it's technically correct. But it's still a more narrow term than "derivative", because functions $f:mathbb{R}^n to mathbb{R}^m,$ with $m>1$, have derivatives but not gradients.
I think using gradient in single variable calculus would just be confusing.
answered Nov 25 at 13:43
B. Goddard
18.3k21340
answered Nov 25 at 13:43
B. Goddard
18.3k21340
answered Nov 25 at 13:43
B. Goddard
18.3k21340
answered Nov 25 at 13:43
B. Goddard
18.3k21340
18.3k21340
add a comment |
add a comment |
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