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Popular Calculus >

derivative of xln^3(x)

Solution

\frac{d}{d x} (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)

Graph

Popular Examples

integral of (11x^3)/(sqrt(9+x^2))

\int \frac{11 x ^{3}}{9 + x ^{2}} d x

integral of 1/((x-3)(x-2))

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

(\partial)/(\partial x)(sqrt(2x^2-5y^2))

\frac{\partial}{\partial x} (2 x^{2} - 5 y^{2})

integral from-2 to 6 of 4x-x^2+12

\int_{- 2}^{6} 4 x - x^{2} + 12 d x

y^{''}+5y^'=e^{-t},y(0)=0,y^'(0)=1

y^{^{''}} + 5 y^{^{'}} = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1

Frequently Asked Questions (FAQ)

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