What is the derivative of w^3ln(3w) ?

The derivative of w^3ln(3w) is 3w^2ln(3w)+w^2

What is the first derivative of w^3ln(3w) ?

The first derivative of w^3ln(3w) is 3w^2ln(3w)+w^2

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derivative of

w^{3} ln (3 w)

3 w^{2} ln (3 w) + w^{2}

Solution steps

\frac{d}{d w} (w^{3} ln (3 w))

Apply the Product Rule:

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

f = w^{3}, g = ln (3 w)

= \frac{d}{d w} (w^{3}) ln (3 w) + \frac{d}{d w} (ln (3 w)) w^{3}

\frac{d}{d w} (w^{3}) = 3 w^{2}

\frac{d}{d w} (ln (3 w)) = \frac{1}{w}

= 3 w^{2} ln (3 w) + \frac{1}{w} w^{3}

\frac{1}{w} w^{3} = w^{2}

= 3 w^{2} ln (3 w) + w^{2}

f (x) = x^{2} - \frac{1}{x}, (1, 0)

\frac{d}{d x} (\frac{1}{9 - x ^{2} - y ^{2} - z ^{2}})

- 2 x e^{- x^{2}}

\frac{\partial}{\partial x} (x^{2} y + x + y)

((x - 1)^{2})^{^{'}}

What is the derivative of w^3ln(3w) ?
The derivative of w^3ln(3w) is 3w^2ln(3w)+w^2
What is the first derivative of w^3ln(3w) ?
The first derivative of w^3ln(3w) is 3w^2ln(3w)+w^2