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Popular >

d/(dw)((wln(w))^2)

Solution

\frac{d}{d w} ((w ln (w))^{2})

Solution

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

Solution steps

\frac{d}{d w} ((w ln (w))^{2})

Simplify

(w ln (w))^{2} : w^{2} ln^{2} (w)

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

Apply the Product Rule:

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

f = w^{2}, g = ln^{2} (w)

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

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

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

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

\frac{2 ln ( w )}{w} w^{2} = 2 w ln (w)

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

Popular Examples

derivative of 32x^{3/2}

\frac{d}{d x} (32 x^{\frac{3}{2}})

tangent of y=arctan(-x),\at x=4 tangent of

y = arctan (- x), at x = 4

derivative of 1/2 x-1/3

\frac{d}{d x} (\frac{1}{2} x - \frac{1}{3})

derivative of y=x^4e^{2x}derivative of

y = x^{4} e^{2 x}

derivative of x^3-6x^2-9

\frac{d}{d x} (x^{3} - 6 x^{2} - 9)

Frequently Asked Questions (FAQ)

What is the d/(dw)((wln(w))^2) ?
The d/(dw)((wln(w))^2) is 2wln^2(w)+2wln(w)
What is the first d/(dw)((wln(w))^2) ?
The first d/(dw)((wln(w))^2) is 2wln^2(w)+2wln(w)