To differentiate y=ax I would use logarithmic differentiation.
1) Take the ln of both sides: ln(y)=ln(ax)
2) Using properties of logs, this equals: ln(y)=x*ln(a)
3) Differentiating each side: y'/y=ln(a)
4) Solving for y': y'=y*ln(a)
5) Substituting for y: y'=ax*ln(a)
The...
For a function such as
w=5xy/z
How would you find the partial derivative of w with respect to y or z? I've tried using basic logarithmic differentiation, but can't arrive at the correct answer. For reference, the correct answer is
wy=5*(xy/z/z)*ln(x)
A certain system can experience three different types of defects. Let A[i] (i=1,2,3) denote the event that the system has a defect of type i. Suppose that
P(A[1]) =.12
P(A[2])=.07
P(A[3])=.05
P(A[1] union A[2])=.13
P(A[1] union A[3])=.14
P(A[2] union A[3])=.10
P(A[1] intersects A[2]...
I'm trying to plot something like x+y=2 in 3D. The image should look like this:
Been trying to do it in Mathematica using Plot3D, but the it treats the input as a function of z.
Another example: Plot3D[x=4,{x,0,10},{y,0,10},AxesLabel{x,y,z}] plots z=4, not x=4.
A similar thread, with no...