What is (d^9)/(x^9)(x^8ln(x)) ?

The solution to (d^9)/(x^9)(x^8ln(x)) is (d^9ln(x))/x

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simplify (d^9)/(x^9)(x^8ln(x))

simplify

\frac{d ^{9}}{x ^{9}} (x^{8} ln (x))

\frac{d ^{9} ln ( x )}{x}

Solution steps

\frac{d ^{9}}{x ^{9}} (x^{8} ln (x))

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{d ^{9}}{x ^{9}} = (\frac{d}{x})^{9}

= (\frac{d}{x})^{9} x^{8} ln (x)

(\frac{d}{x})^{9} = \frac{d ^{9}}{x ^{9}}

= \frac{d ^{9}}{x ^{9}} x^{8} ln (x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{d ^{9} x ^{8} ln ( x )}{x ^{9}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{x ^{8}}{x ^{9}} = \frac{1}{x ^{9 - 8}}

= \frac{d ^{9} ln ( x )}{x ^{9 - 8}}

Subtract the numbers:

9 - 8 = 1

= \frac{d ^{9} ln ( x )}{x}

2 6^{2}

\frac{d}{d x} (x^{2} + y^{2})

x \cdot x + 1

3^{6}

[(2 π)^{2}]^{2}

What is (d^9)/(x^9)(x^8ln(x)) ?
The solution to (d^9)/(x^9)(x^8ln(x)) is (d^9ln(x))/x