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Popular >

derivative of y=xln^3(x)

Solution

derivative of

y = x ln^{3} (x)

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot ln^{3} (x) + \frac{3 ln ^{2} ( x )}{x} x : ln^{3} (x) + 3 ln^{2} (x)

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

Popular Examples

(\partial)/(\partial x)(x-x^2y-y+xy^2)

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

limit as x approaches 0 of x^7sin(1/x)

x \to 0 lim (x^{7} sin (\frac{1}{x}))

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(9 - \frac{x}{9})^{- 7}

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implicit (dy)/(dx),6x^2+3xy+2y^2+17y-6=0 implicit derivative

\frac{d y}{d x}, 6 x^{2} + 3 x y + 2 y^{2} + 17 y - 6 = 0

Frequently Asked Questions (FAQ)

What is the derivative of y=xln^3(x) ?
The derivative of y=xln^3(x) is ln^3(x)+3ln^2(x)
What is the first derivative of y=xln^3(x) ?
The first derivative of y=xln^3(x) is ln^3(x)+3ln^2(x)