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

The derivative of ((x^4+2))/(ln(x)) is (4x^4ln(x)-x^4-2)/(xln^2(x))

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

The first derivative of ((x^4+2))/(ln(x)) is (4x^4ln(x)-x^4-2)/(xln^2(x))

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

Simplify

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

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

\frac{\partial}{\partial x} (e^{- x y})

n = 0 \sum \infty n^{2} x^{n}

\int (3 x + 2)^{4} d x

\frac{d}{d x} (e^{2 x} sin (6 x))

\frac{d}{d x} (\frac{4 x - 12}{( x - 2 ) ^{2}})

What is the derivative of ((x^4+2))/(ln(x)) ?
The derivative of ((x^4+2))/(ln(x)) is (4x^4ln(x)-x^4-2)/(xln^2(x))
What is the first derivative of ((x^4+2))/(ln(x)) ?
The first derivative of ((x^4+2))/(ln(x)) is (4x^4ln(x)-x^4-2)/(xln^2(x))