What is the derivative of (x^2ln(x^{(55}))^{(1/3)}) ?

The derivative of (x^2ln(x^{(55}))^{(1/3)}) is (55^{1/3}(2ln(x)+1))/(3x^{1/3)ln^{2/3}(x)}

What is the first derivative of (x^2ln(x^{(55}))^{(1/3)}) ?

The first derivative of (x^2ln(x^{(55}))^{(1/3)}) is (55^{1/3}(2ln(x)+1))/(3x^{1/3)ln^{2/3}(x)}

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\frac{d}{d x} ((x^{2} ln (x^{(55)}))^{(\frac{1}{3})})

\frac{5 5 ^{\frac{1}{3}} ( 2 ln ( x ) + 1 )}{3 x ^{\frac{1}{3}} ln ^{\frac{2}{3}} ( x )}

Solution steps

\frac{d}{d x} ((x^{2} ln (x^{(55)}))^{(\frac{1}{3})})

Apply the chain rule:

\frac{1}{3 ( x ^{2} ln ( x ^{55} ) ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} ln (x^{55}))

= \frac{1}{3 ( x ^{2} ln ( x ^{55} ) ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} ln (x^{55}))

\frac{d}{d x} (x^{2} ln (x^{55})) = 2 x ln (x^{55}) + 55 x

= \frac{1}{3 ( x ^{2} ln ( x ^{55} ) ) ^{\frac{2}{3}}} (2 x ln (x^{55}) + 55 x)

Simplify

\frac{1}{3 ( x ^{2} ln ( x ^{55} ) ) ^{\frac{2}{3}}} (2 x ln (x^{55}) + 55 x) : \frac{5 5 ^{\frac{1}{3}} ( 2 ln ( x ) + 1 )}{3 x ^{\frac{1}{3}} ln ^{\frac{2}{3}} ( x )}

= \frac{5 5 ^{\frac{1}{3}} ( 2 ln ( x ) + 1 )}{3 x ^{\frac{1}{3}} ln ^{\frac{2}{3}} ( x )}

\frac{\partial}{\partial x} (A e^{- b (A, x, v, t) (x - v t)^{2}})

\frac{d}{d x} (\frac{d y}{d x}) + 25 y = 0

x \to 0 lim (\frac{sin ^{9} ( x )}{x})

\int x^{2} e^{x^{3} + 4} d x

f (x) = \frac{( x ^{2} - 1 )}{( x ^{2} + 1 )}

What is the derivative of (x^2ln(x^{(55}))^{(1/3)}) ?
The derivative of (x^2ln(x^{(55}))^{(1/3)}) is (55^{1/3}(2ln(x)+1))/(3x^{1/3)ln^{2/3}(x)}
What is the first derivative of (x^2ln(x^{(55}))^{(1/3)}) ?
The first derivative of (x^2ln(x^{(55}))^{(1/3)}) is (55^{1/3}(2ln(x)+1))/(3x^{1/3)ln^{2/3}(x)}