A contour of the magnetic potential U U\,U in a specialized laboratory setup is modeled by the curve with equation
x5y+4xy5=130 x^5 y + 4x y^5 = 130 x5y+4xy5=130Prove that the curve does not intersect the coordinate axes.
Show that
dydx=−5x4y+4y5x5+20xy4 \frac{dy}{dx} = -\frac{5x^4 y + 4y^5}{x^5 + 20xy^4} dxdy=−x5+20xy45x4y+4y5Prove that the curve has no stationary points.
In the case when x>0x > 0x>0, find the equation of the tangent line to the curve at the point where y=2y = 2y=2. Give your answer in the form ay+bx=cay + bx = cay+bx=c, where a,b,c a, b, c\,a,b,c are integers.
Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
