What is the derivative of x(1-2y) ?

The derivative of x(1-2y) is 1-2y-2x(dy)/(dx)

What is the first derivative of x(1-2y) ?

The first derivative of x(1-2y) is 1-2y-2x(dy)/(dx)

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

1 - 2 y - 2 x \frac{d y}{d x}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 1 - 2 y

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

\frac{d x}{d x} = 1

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

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

Simplify

= 1 - 2 y - 2 x \frac{d y}{d x}

\frac{25 x ^{3}}{3} + 10 x^{2} + 4 x - 7

f (x) = \frac{2}{x + 3}

\frac{\partial}{\partial y} (x^{y} ln (x))

\int_{0}^{34} x^{2} - 17 d x

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

What is the derivative of x(1-2y) ?
The derivative of x(1-2y) is 1-2y-2x(dy)/(dx)
What is the first derivative of x(1-2y) ?
The first derivative of x(1-2y) is 1-2y-2x(dy)/(dx)