What is the derivative of-y^2x ?

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = y^{2}, g = x

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

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

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

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

Simplify

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

\int cos (2 θ) d θ

f (x) = 3 x^{2} + 2 a x + b

y^{^{''}} - 2 y^{^{'}} + 5 y = 5 x + 3

x \to 3 lim (\frac{3 - x}{∣ x - 3 ∣})

\int (8 x + 1 - 9 e^{x}) d x

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