y=6(sqrt x) + 3/x^2 +10    (x not equal 0) find dy/dx?
360927
y'=dy/dx=\n\n(6√x)' + (3/x^2)' + (10)'=\n\n[6*x^(1/2)]' + [3x^(-2)]' + 0= \nnow use the power rule\n\n6*(1/2)* x^[(1/2)-1] + 3*(-2)*x^(-2-1)=\n\n3*x^(-1/2)-6x^(-3)=\n\n3/x^(1/2) -6/x^3=\n\n3/√x - 6/x^3
667880
a) dy/dx = x - 1/x^2\ndy = (x-x^(-2))dx\ny = x^2/2 + 1/x + C\ny(1) = 1^2/2 + 1/1 + C = 2\n1/2 + 1 + C = 2 implies C = 1/2\nAnswer: y = x^2/2 + 1/x + 1/2, x>0\n\nb) The integration is already finished.  Just plug in -1 for x.\ny(-1) = (-1)^2/2 + 1/-1 + C = 1\n-1/2 - 1 + C = 1 implies C = 3/2\nAnswer: x^2/2 + 1/x + 3/2, x<0\n\nc) Just take the derivative of each one.  C1 and C2 are constants, so their derivative is 0.  \n\nd) C1 = 1/2 and C2 = 3/2\n\ne) Follow parts (a) and (b) except plug in 2 for x and set it equal to -1.  Similarly for y(-2) = 2.\nCheck that C1 = -7/2 and C2 = 1/2
1139627
dy/dx = 2x-3\nat X = 0. dy/dx = 2(0) -3 = -3
801041
Notice x = -3 + 3y (based on your second equation), so substitute this for x into your first equation to solve for y:\n\n-2x + 7y = 10\n\n-2(-3 + 3y) + 7y = 10\n\n6 - 6y + 7y = 10\n\n6 + y = 10\n\ny = 4\n\nNow plug this into the other equation to solve for x:\n\nx = -3 + 3y\n\nx = -3 + 3(4)\n\nx = -3 + 12\n\nx = 9\n\nANSWER:  x=9, y=4\n\nNRT
752053
Let say x is y, to avoid any confusion.\n3/y = (y + 5)/2\n\nMultiply by 2 at both side.\n3/y x 2 = (y + 5)/2 x 2\n6/y = y + 5\n\nMultiply by y at both side.\n6/y x y = y x (y + 5)\n6 = y(y + 5)\n6 = y^2 + 5y\n\nBring all the numbers to one side.\ny^2 + 5y - 6 = 0\n\nFactorize the equation.\n(y + 6)(y - 1) = 0\n\nTherefore,\ny + 6 = 0  or  y - 1 = 0\ny = -6  or  y = 1\n\nIn short,\ny = -6, 1\n\nAs I had mentioned earlier, x = y.  \nTherefore, x = -6, 1.
836011
dP/dt=dP/dx/dx/dt\ndP/dx=d/dx of Profit\n=d/dx of [-0.4x^2+24x-10]\n=-0.8x+24\n=-0.8(25)+24\n=4\ndx/dt=6\ndP/dx/dt/dx\n=4*6=24
374950
Plug in x, solve for y as follows:\nIf x=0 then solve for y and get y= 3/2\nif x=10 y= -10/2+ 3/2 = -7/2\nCreate a graph using the horizontal as the x scale and the vertical as y.  Plot the above and you will see that it's a straight line.
718048
x + y = 3\n\nSolve for a variable.  I chose X.\nx+y = 3\n -y    -y\nx = 3 - y\n\nSubstitute the value of X in the first equation.\n2(3-y) + y = 4\nDistribute.\n6-2y+y = 4\nAdd like terms.\n6-y = 4\n-6    -6\n-y = -2\nmultiply by -1.\ny=2\n\nSince you know Y = 2, substitute that back into the second equation that you solved for X with.\nx + y = 3\nX + 2 = 3\n  -2    -2\nX = 1\n\nX = 1\nY = 2
349210
dy/dx = -(15cos(3/x)/2x^2) * (sin(3/x))^3/2
948239
xy = y^½\n y = y^½ /x\n y = y^½*x^-½\n\ndy/dx = -½ y^½ x^ -3/2\ndy/dx = - [½ y^½ ]/x^+3/2\ndy/dx = - (y^½) / (2x^3/2)
754733
Let y = u/v   where u=some function and v =some funtion\n\nthen dy/dx = (v*du/dx - u*dv/dx)/ (v^2)     **Quotient Rule**\n\nIn this case u = 6x^2-1 and v = 2*sqrt(x)\n\nSo you just differentiate and plug into the equation for dy/dx
395515
6x+2y=10\nsubract 6x fro both sides\n2y=-2x+10\ndivide both sides by 2\ny=-x+5
87883
First write y as a product instead of a quotient:\n\n(2+x)*(2-3x)^(-1)\n\nNow you should be able to do this. \nUse 2+x as your f and (2-3x)^(-1) as your g. \nYou will have to use the chain rule to find g'.
1082168
y=x^2+10x+8\ny=(x+5)^2 - 17\n\nVertex form: (5,-17)
70526
=((-4y)^2)/(10y-5)= (16y^2)/(10y-5)\nand if the equation is equal to zero then y=4i
731860
x² - y² = 16\nSo 2x - 2ydy/dx = 0\nie dy/dx = x/y\n\nd²y/dx² = (y - xdy/dx)/y² (NOTE: x² - y² = 16  → y² = x² - 16)\n= (y - x.x/y)/(x² - 16)\n= (y² - x²)/(x²y - 16y)\n= -16/(x²y - 16y) (As x² - y² = 16)
1144370
This is a homogeneous differential equation.  \ndy/dx - y/x = x/y\ndy/dx = x/y + y/x \ndy/dx = (1/(x/y)) + y/x\nLet,\nv = y/x\ny = xv\ndy/dx = v + (x)(dv/dx)\nPlugging this back into the above equation we get,\nv + (x)(dv/dx) = 1/v + v\n (x)(dv/dx) = 1/v [canceling v out of both sides]\n1/x dx = v dv [rearranging]\nln(x) + c = 1/2 (v^2) [integrating both sides]\n2 ln(x) + c = v^2\nln(x^2) +c = (y/x)^2 [using log law and substituting value of v back into the equation]\nln(x^2) + c = y^2/x^2\ny^2 = (x^2)(ln(x^2)) + c(x^2)\nSolved!