What is the derivative of 4xy^3 ?

The derivative of 4xy^3 is 4(y^3+3xy^2(dy)/(dx))

What is the first derivative of 4xy^3 ?

The first derivative of 4xy^3 is 4(y^3+3xy^2(dy)/(dx))

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\frac{d}{d x} (4 x y^{3})

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

Solution steps

\frac{d}{d x} (4 x y^{3})

Take the constant out:

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

= 4 \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}

= 4 (\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}

= 4 (1 \cdot y^{3} + 3 y^{2} \frac{d y}{d x} x)

Simplify

= 4 (y^{3} + 3 x y^{2} \frac{d y}{d x})

x (9.3)

y^{^{'}} = - \frac{y}{t} + 2

f (x) = x^{4} - 4 x^{2}, g (x) = x^{2} - 4

\int (6 x + 2) d x

x \to - \infty lim (arccot (x))

What is the derivative of 4xy^3 ?
The derivative of 4xy^3 is 4(y^3+3xy^2(dy)/(dx))
What is the first derivative of 4xy^3 ?
The first derivative of 4xy^3 is 4(y^3+3xy^2(dy)/(dx))