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

The derivative of sqrt((x^4/(ln(x)))) is (x(4ln(x)-1))/(2ln^{3/2)(x)}

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

The first derivative of sqrt((x^4/(ln(x)))) is (x(4ln(x)-1))/(2ln^{3/2)(x)}

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

\frac{x ( 4 ln ( x ) - 1 )}{2 ln ^{\frac{3}{2}} ( x )}

Solution steps

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

Apply the chain rule:

\frac{1}{2 \frac{x ^{4}}{l n ( x )}} \frac{d}{d x} (\frac{x ^{4}}{ln ( x )})

= \frac{1}{2 \frac{x ^{4}}{l n ( x )}} \frac{d}{d x} (\frac{x ^{4}}{ln ( x )})

\frac{d}{d x} (\frac{x ^{4}}{ln ( x )}) = \frac{4 x ^{3} ln ( x ) - x ^{3}}{ln ^{2} ( x )}

= \frac{1}{2 \frac{x ^{4}}{l n ( x )}} \cdot \frac{4 x ^{3} ln ( x ) - x ^{3}}{ln ^{2} ( x )}

Simplify

\frac{1}{2 \frac{x ^{4}}{l n ( x )}} \cdot \frac{4 x ^{3} ln ( x ) - x ^{3}}{ln ^{2} ( x )} : \frac{x ( 4 ln ( x ) - 1 )}{2 ln ^{\frac{3}{2}} ( x )}

= \frac{x ( 4 ln ( x ) - 1 )}{2 ln ^{\frac{3}{2}} ( x )}

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

e^{- h} + e^{h}

20 (1 + e^{10 - t})^{- 1}

y^{^{'}} = 8 x y

\int \frac{4}{x ^{2} x ^{2} + 25} d x

What is the derivative of sqrt((x^4/(ln(x)))) ?
The derivative of sqrt((x^4/(ln(x)))) is (x(4ln(x)-1))/(2ln^{3/2)(x)}
What is the first derivative of sqrt((x^4/(ln(x)))) ?
The first derivative of sqrt((x^4/(ln(x)))) is (x(4ln(x)-1))/(2ln^{3/2)(x)}