What is the derivative of 2sqrt(xy) ?

The derivative of 2sqrt(xy) is (y+x\frac{dy)/(dx)}{sqrt(xy)}

What is the first derivative of 2sqrt(xy) ?

The first derivative of 2sqrt(xy) is (y+x\frac{dy)/(dx)}{sqrt(xy)}

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

\frac{y + x \frac{d y}{d x}}{x y}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

\frac{1}{2 x y} \frac{d}{d x} (x y)

= \frac{1}{2 x y} \frac{d}{d x} (x y)

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

= 2 \cdot \frac{1}{2 x y} (y + x \frac{d y}{d x})

Simplify

2 \cdot \frac{1}{2 x y} (y + x \frac{d y}{d x}) : \frac{y + x \frac{d y}{d x}}{x y}

= \frac{y + x \frac{d y}{d x}}{x y}

x^{^{'}} = 6 (x^{2} + 1)

\frac{d}{d x} (1 0^{x^{2}})

\int_{0}^{4} \frac{1}{9 + x ^{2}} d x

\frac{\partial}{\partial x} (- 6 x + 12)

y^{2} = 4 x, y = 4 x - 2

What is the derivative of 2sqrt(xy) ?
The derivative of 2sqrt(xy) is (y+x\frac{dy)/(dx)}{sqrt(xy)}
What is the first derivative of 2sqrt(xy) ?
The first derivative of 2sqrt(xy) is (y+x\frac{dy)/(dx)}{sqrt(xy)}