What is the derivative of (x^2ln(x)^4) ?

The derivative of (x^2ln(x)^4) is 8x^7ln^4(x)+4x^7ln^3(x)

What is the first derivative of (x^2ln(x)^4) ?

The first derivative of (x^2ln(x)^4) is 8x^7ln^4(x)+4x^7ln^3(x)

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\frac{d}{d x} ((x^{2} ln (x))^{4})

8 x^{7} ln^{4} (x) + 4 x^{7} ln^{3} (x)

Solution steps

\frac{d}{d x} ((x^{2} ln (x))^{4})

Simplify

(x^{2} ln (x))^{4} : x^{8} ln^{4} (x)

= \frac{d}{d x} (x^{8} ln^{4} (x))

Apply the Product Rule:

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

f = x^{8}, g = ln^{4} (x)

= \frac{d}{d x} (x^{8}) ln^{4} (x) + \frac{d}{d x} (ln^{4} (x)) x^{8}

\frac{d}{d x} (x^{8}) = 8 x^{7}

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

= 8 x^{7} ln^{4} (x) + \frac{4 ln ^{3} ( x )}{x} x^{8}

\frac{4 ln ^{3} ( x )}{x} x^{8} = 4 x^{7} ln^{3} (x)

= 8 x^{7} ln^{4} (x) + 4 x^{7} ln^{3} (x)

What is the derivative of (x^2ln(x)^4) ?
The derivative of (x^2ln(x)^4) is 8x^7ln^4(x)+4x^7ln^3(x)
What is the first derivative of (x^2ln(x)^4) ?
The first derivative of (x^2ln(x)^4) is 8x^7ln^4(x)+4x^7ln^3(x)