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Popular >

derivative of 3x^2+2xy-y^2

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (3 x^{2}) = 6 x

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

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

= 6 x + 2 (y + x \frac{d y}{d x}) - 2 y \frac{d y}{d x}

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\int \frac{e ^{x} + 1}{e ^{x} - 1} d x

Frequently Asked Questions (FAQ)

What is the derivative of 3x^2+2xy-y^2 ?
The derivative of 3x^2+2xy-y^2 is 6x+2(y+x(dy)/(dx))-2y(dy)/(dx)
What is the first derivative of 3x^2+2xy-y^2 ?
The first derivative of 3x^2+2xy-y^2 is 6x+2(y+x(dy)/(dx))-2y(dy)/(dx)