What is the derivative of-yx ?

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

What is the first derivative of-yx ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = y, g = x

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

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

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

Simplify

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

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