What is the derivative of y^2-x^3+8 ?

The derivative of y^2-x^3+8 is -3x^2+2y(dy)/(dx)

What is the first derivative of y^2-x^3+8 ?

The first derivative of y^2-x^3+8 is -3x^2+2y(dy)/(dx)

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

- 3 x^{2} + 2 y \frac{d y}{d x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (y^{2}) = 2 y \frac{d y}{d x}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (8) = 0

= 2 y \frac{d y}{d x} - 3 x^{2} + 0

Simplify

= - 3 x^{2} + 2 y \frac{d y}{d x}

What is the derivative of y^2-x^3+8 ?
The derivative of y^2-x^3+8 is -3x^2+2y(dy)/(dx)
What is the first derivative of y^2-x^3+8 ?
The first derivative of y^2-x^3+8 is -3x^2+2y(dy)/(dx)