How to do implicit differentiation

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The graph shows a circle centred at the origin with a radius of 5.

a) Define the circle implicitly by a relation between x and y .
b) Define the circle by expressing y explicitly in terms of x .
c) Use the method of "explicit differentiation" to find the slope of the tangent line to the circle at the point (4, -3).
d) Use the method of "implicit differentiation" to find the slope of the tangent line to the circle at the point (4, -3).
$3{y^4} + 5{x^2}{y^3} - {x^6} = 2x - 9y + 1$ $3 y^{4} + 5 x^{2} y^{3} - x^{6} = 2 x - 9 y + 1$
Use implicit differentiation to find: $\frac{{{d}y}}{{{d}x}}$ $\frac{d y}{d x}$

Implicit differentiation