Oct 19, 2016 · y = C_1e^x-x-1 Let u = x + y => (du)/dx = d/dx(x+y) = 1+dy/dx => dy/dx = (du)/dx-1 Thus, making the substitutions into our original equation, (du)/dx-1 = u => (du ...

Jul 1, 2016 · How do you use implicit differentiation to find #y'# for #sin(xy) = 1#? How do you find the second derivative by implicit differentiation on #x^3y^3=8# ? What is the derivative of …

Mar 23, 2018 · See explanation Consider y=x The count of x's is 1 so although it is not normally shown we actually have y=+1x This number 1 is the slope (gradient) which is the amount of up …

Mar 21, 2018 · (x+y)^4 = x^4+y^4+z^4+4x^3y+4xy^3+4y^3z+4yz^3+4z^3x+4zx^3+6x^2y^2+6y^2z^2+6z^2x^2+12x^2yz+12xy^2z+12xyz^2 …

Sep 1, 2015 · The row of Pascal's triangle starting 1, 6 gives the sequence of coefficients for the binomial expansion. Write out Pascal's triangle as far as the row that begins 1, 6 ... These are …

Mar 3, 2017 · See below. The pass equations are {(x = r cos theta),(y=r sintheta):} so x = y -> rcostheta=rsintheta or forall r ->costheta=sintheta->tantheta=1->theta = pi/4 + k pi so in polar …

Aug 31, 2015 · Anyway, I mean the row that starts 1, 7... Each number is formed by adding the two numbers above to the left and right. The last row gives us the coefficients we need: …

Sep 18, 2016 · Consider Pascal's Triangle, as shown in the following diagram: The expansion of the above binomial will have n + 1 terms, in (A + B)^n. So, our binomial expansion will have 10 …

Jul 23, 2016 · 1/2 ln((y/x)^2+1) - arctan (y/x) = - ln x + C dy/dx=(x+y)/(x-y) this is first order linear and homogeneous in the sense that when written in the form dy/dx = f(x,y) then f(kx, ky) = …

Apr 17, 2018 · You are probably familiar with the x-y Cartesian Coordinate system. This is a 2-dimensional flat plane and locations on the plane can be identified by an (x,y) Coordinate. Z …