What is the derivative of-xy^3 ?

The derivative of-xy^3 is -y^3-3xy^2(dy)/(dx)

What is the first derivative of-xy^3 ?

The first derivative of-xy^3 is -y^3-3xy^2(dy)/(dx)

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

- y^{3} - 3 x y^{2} \frac{d y}{d x}

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = y^{3}

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

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

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

= - (1 \cdot y^{3} + 3 y^{2} \frac{d y}{d x} x)

Simplify

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

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

(- 2, 4), (- 1, - 1)

\int_{- a}^{a} (a - ∣ x ∣) d x

a \to 0 lim (x^{a})

\frac{x + 7}{x + 1}

y = 4 x^{3} - 4 x, (1, 0)

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