What is the slope of (2x+2y)^3=8x^3+8y^3 ?

The slope of (2x+2y)^3=8x^3+8y^3 is -(y(2x+y))/(x(x+2y))

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slope of (2x+2y)^3=8x^3+8y^3

slope

(2 x + 2 y)^{3} = 8 x^{3} + 8 y^{3}

- \frac{y ( 2 x + y )}{x ( x + 2 y )}

Solution steps

(2 x + 2 y)^{3} = 8 x^{3} + 8 y^{3}

Use implicit differentiation to find the slope of

(2 x + 2 y)^{3} = 8 x^{3} + 8 y^{3}

Implicit Derivative

\frac{d y}{d x}

(2 x + 2 y)^{3} = 8 x^{3} + 8 y^{3} : - \frac{y ( 2 x + y )}{x ( x + 2 y )}

- \frac{y ( 2 x + y )}{x ( x + 2 y )}

\int (\frac{tan ( x )}{sin ( x ) cos ( x )}) d x

f (x) \frac{3}{x}

f (x) = 2 x^{2} + 3, x, [- 1, 2]

x \to - 2 lim (x^{2} + x - 2)

f (x) = 2 x^{2} - x + 1, at x = 1

What is the slope of (2x+2y)^3=8x^3+8y^3 ?
The slope of (2x+2y)^3=8x^3+8y^3 is -(y(2x+y))/(x(x+2y))