What is the derivative of #7xy#?

Answer 1
That depends on what variable you want to take the derivative with respect to. With respect to #x# the answer is #7*y#, while with respect to #y# the answer is #7*x#.
When you take a derivative of a function you get an expression that represents the rate of change or slope of that function. With single variable calculus you usually only ever take derivatives for a function with respect to the independent variable. This is usually represented by #x#. However, with multivariate calculus you often times have a function defined in three or more dimensions. For instance the above function might look something like this.
#z=7*x*y#
You could then choose to take the derivative with respect to either the #x# axis or the #y# axis. If you take the derivative with respect to the #y# axis you will get an expression representing the rate of change or slope in the #y# direction, while if you were instead take the derivative with respect to the #x# axis you would get an expression representing the slope in the #x# direction. The process to take that derivative is as simple as treating the other variable as if it were a constant like the #7#.
#(dz)/(dy)=7*x#
#(dz)/(dx)=7*y#
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Answer 2
#(7xy)'=7xy' + 7y#

To get this we use the product rule:

#d((uv))/(dx)=u.(dv)/(dx)+v.(du)/(dx)#
So #d((7xy))/(dx) = 7x.dy/dx+ 7y.dx/dx#

Which we can write:

#(7xy)'=7xy'+7y#

or

#(7xy)'=7(xy'+y)#
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Answer 3

The derivative of (7xy) with respect to (x) is (7y), and with respect to (y) is (7x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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