MathsQuestions

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$x^2 y^2 + x = y$$

$\dfrac{2xy^2 + 1}{1 - 2x^2 y}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$x^3 + 3x^2 y + y^3 = 5$$

$-\dfrac{x^2 + 2xy}{x^2 + y^2}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$(x + y)^3 = x^2$$

$\dfrac{2x - 3(x+y)^2}{3(x+y)^2}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$x^2 - 3xy + 2y^2 = 4$$

$\dfrac{3y - 2x}{4y - 3x}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$xy^2 - x^2 y = 2$$

$\dfrac{2xy - y^2}{2xy - x^2}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$\sqrt{x} + \sqrt{y} = 4$$

$-\sqrt{\dfrac{y}{x}}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y^3 - 3xy = 2$$

$\dfrac{y}{y^2 - x}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$x^3 + y^3 = 9xy$$

$\dfrac{3y - x^2}{y^2 - 3x}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$x^2 y + xy^2 = 6$$

$-\dfrac{2xy + y^2}{x^2 + 2xy}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$x^3 - xy + y^3 = 0$$

$\dfrac{y - 3x^2}{3y^2 - x}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = (x + y)^3$$

$\dfrac{3(x+y)^2}{1 - 3(x+y)^2}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$x^2 + 2xy - y^2 = 4$$

$\dfrac{x+y}{y-x}$

Find the coordinates of the points on the curve $$x^2 + y^2 = 25$$ where the tangent is parallel to the $x$-axis.

$(0, 5)$ and $(0, -5)$

Find the coordinates of the points on the curve $$x^2 + y^2 = 25$$ where the tangent is parallel to the $y$-axis.

$(5, 0)$ and $(-5, 0)$

Find the coordinates of the points on the curve $$4x^2 + 9y^2 = 36$$ where the tangent is parallel to the $x$-axis.

$(0, 2)$ and $(0, -2)$

Find the coordinates of the points on the curve $$4x^2 + 9y^2 = 36$$ where the tangent is parallel to the $y$-axis.

$(3, 0)$ and $(-3, 0)$

Find the coordinates of the points on the curve $$x^2 + xy + y^2 = 12$$ where the tangent is parallel to the $x$-axis.

$(2, -4)$ and $(-2, 4)$

Find the coordinates of the points on the curve $$x^2 + xy + y^2 = 12$$ where the tangent is parallel to the $y$-axis.

$(-4, 2)$ and $(4, -2)$

Find the coordinates of the points on the curve $$x^2 - xy + y^2 = 3$$ where the tangent is parallel to the $x$-axis.

$(1, 2)$ and $(-1, -2)$

Find the coordinates of the points on the curve $$x^2 - xy + y^2 = 3$$ where the normal is parallel to the $x$-axis.

$(2, 1)$ and $(-2, -1)$

Find the coordinates of the points on the curve $$x^2 + y^2 = 36$$ where the normal is parallel to the $y$-axis.

$(0, 6)$ and $(0, -6)$

Find the coordinates of the points on the curve $$x^2 + 4y^2 = 4$$ where the normal is parallel to the $x$-axis.

$(2, 0)$ and $(-2, 0)$

Find the coordinates of the points on the curve $$y^2 = x^3 - 12x$$ where the tangent is parallel to the $x$-axis.

$(-2, 4)$ and $(-2, -4)$

Find the coordinates of the points on the curve $$x^2 - y^2 = 16$$ where the tangent is parallel to the $y$-axis.

$(4, 0)$ and $(-4, 0)$

Find the equation of the tangent to the curve $$x^2 + xy + y^2 = 7$$ at the point $(1, 2)$.

$4x + 5y = 14$

Find the equation of the normal to the curve $$x^2 - y^2 = 9$$ at the point $(5, 4)$.

$4x + 5y = 40$

Find the equation of the normal to the curve $$x^2 + y^2 = 25$$ at the point $(3, 4)$.

$y = \dfrac{4}{3}x$

Find the equation of the tangent to the curve $$y^2 = x^3$$ at the point $(1, 1)$.

$3x - 2y = 1$

Find the equation of the tangent to the curve $$x^3 + y^3 = 9xy$$ at the point $(2, 4)$.

$5y = 4x + 12$

Find the equation of the normal to the curve $$xy = 8$$ at the point $(2, 4)$.

$2y = x + 6$