What is the derivative of (x^4ln(x)^5) ?

The derivative of (x^4ln(x)^5) is 20x^{19}ln^5(x)+5x^{19}ln^4(x)

What is the first derivative of (x^4ln(x)^5) ?

The first derivative of (x^4ln(x)^5) is 20x^{19}ln^5(x)+5x^{19}ln^4(x)

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\frac{d}{d x} ((x^{4} ln (x))^{5})

20 x^{19} ln^{5} (x) + 5 x^{19} ln^{4} (x)

Solution steps

\frac{d}{d x} ((x^{4} ln (x))^{5})

Simplify

(x^{4} ln (x))^{5} : x^{20} ln^{5} (x)

= \frac{d}{d x} (x^{20} ln^{5} (x))

Apply the Product Rule:

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

f = x^{20}, g = ln^{5} (x)

= \frac{d}{d x} (x^{20}) ln^{5} (x) + \frac{d}{d x} (ln^{5} (x)) x^{20}

\frac{d}{d x} (x^{20}) = 20 x^{19}

\frac{d}{d x} (ln^{5} (x)) = \frac{5 ln ^{4} ( x )}{x}

= 20 x^{19} ln^{5} (x) + \frac{5 ln ^{4} ( x )}{x} x^{20}

\frac{5 ln ^{4} ( x )}{x} x^{20} = 5 x^{19} ln^{4} (x)

= 20 x^{19} ln^{5} (x) + 5 x^{19} ln^{4} (x)

x \to 6 lim (ln (6 - x))

x \to 0 lim (x - \frac{1}{x})

x \to 0 + lim (4 sin (x) ln (x))

\frac{1}{1 + x ^{2}}

x \to 3 lim (\frac{- 4}{2 x - 5})

What is the derivative of (x^4ln(x)^5) ?
The derivative of (x^4ln(x)^5) is 20x^{19}ln^5(x)+5x^{19}ln^4(x)
What is the first derivative of (x^4ln(x)^5) ?
The first derivative of (x^4ln(x)^5) is 20x^{19}ln^5(x)+5x^{19}ln^4(x)