dy/dx=(-8xy^2+4x)(4x+1)y-(8x^3+4x^2-1)
El resultado
To solve this problem, we need to apply the techniques of differential calculus. Let's break it down step by step:
Step 1: Simplify the given equation.
dy/dx = (-8xy^2+4x)(4x+1)y - (8x^3+4x^2-1)
Step 2: Expand and simplify the equation further.
dy/dx = (-32x^2y^3 - 8xy^2 + 4x^2y + x)(4x+1)y - (8x^3+4x^2-1)
Step 3: Distribute the y term throughout the first bracket.
dy/dx = (-32x^2y^4 - 8xy^3 + 4x^2y^2 + xy)(4x+1) - (8x^3+4x^2-1)
Step 4: Multiply the entire equation out.
dy/dx = -128x^3y^4 - 32x^2y^3 + 16x^3y^2 + 4x^2y - 32x^2y^4 - 8xy^3 + 4x^2y^2 + xy - 8x^3 - 4x^2 + 1
At this stage, we have simplified the equation as much as possible.
Please note that this is the simplified form of the equation dy/dx = (-8xy^2+4x)(4x+1)y-(8x^3+4x^2-1).