What is the derivative of ln(x^3(x-1)^4) ?

The derivative of ln(x^3(x-1)^4) is (3(x-1)^4)/x+12ln(x)(x-1)^3

What is the first derivative of ln(x^3(x-1)^4) ?

The first derivative of ln(x^3(x-1)^4) is (3(x-1)^4)/x+12ln(x)(x-1)^3

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\frac{d}{d x} (ln (x^{3}) (x - 1)^{4})

\frac{3 ( x - 1 ) ^{4}}{x} + 12 ln (x) (x - 1)^{3}

Solution steps

\frac{d}{d x} (ln (x^{3}) (x - 1)^{4})

Apply the Product Rule:

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

f = ln (x^{3}), g = (x - 1)^{4}

= \frac{d}{d x} (ln (x^{3})) (x - 1)^{4} + \frac{d}{d x} ((x - 1)^{4}) ln (x^{3})

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

\frac{d}{d x} ((x - 1)^{4}) = 4 (x - 1)^{3}

= \frac{3}{x} (x - 1)^{4} + 4 (x - 1)^{3} ln (x^{3})

Simplify

\frac{3}{x} (x - 1)^{4} + 4 (x - 1)^{3} ln (x^{3}) : \frac{3 ( x - 1 ) ^{4}}{x} + 12 ln (x) (x - 1)^{3}

= \frac{3 ( x - 1 ) ^{4}}{x} + 12 ln (x) (x - 1)^{3}

\int 2 \cdot e^{2 x} d x

x \to 0 lim (\frac{1}{sin ( 3 x )})

f (x) = 2 x^{2}, at 3

\int_{- 2}^{3} \frac{12}{x ^{4}} d x

f (x) = sin (sin (x)), at x = 3 π

What is the derivative of ln(x^3(x-1)^4) ?
The derivative of ln(x^3(x-1)^4) is (3(x-1)^4)/x+12ln(x)(x-1)^3
What is the first derivative of ln(x^3(x-1)^4) ?
The first derivative of ln(x^3(x-1)^4) is (3(x-1)^4)/x+12ln(x)(x-1)^3