What is the derivative of y=ln(1/(xsqrt(x-10))) ?

The derivative of y=ln(1/(xsqrt(x-10))) is -(3x-20)/(2x(x-10))

What is the first derivative of y=ln(1/(xsqrt(x-10))) ?

The first derivative of y=ln(1/(xsqrt(x-10))) is -(3x-20)/(2x(x-10))

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derivative of

y = ln (\frac{1}{x x - 10})

- \frac{3 x - 20}{2 x ( x - 10 )}

Solution steps

\frac{d}{d x} (ln (\frac{1}{x x - 10}))

Simplify

ln (\frac{1}{x x - 10}) : - ln (x x - 10)

= \frac{d}{d x} (- ln (x x - 10))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (ln (x x - 10))

Apply the chain rule:

\frac{1}{x x - 10} \frac{d}{d x} (x x - 10)

= \frac{1}{x x - 10} \frac{d}{d x} (x x - 10)

\frac{d}{d x} (x x - 10) = \frac{3 x - 20}{2 x - 10}

= - \frac{1}{x x - 10} \cdot \frac{3 x - 20}{2 x - 10}

Simplify

- \frac{1}{x x - 10} \cdot \frac{3 x - 20}{2 x - 10} : - \frac{3 x - 20}{2 x ( x - 10 )}

= - \frac{3 x - 20}{2 x ( x - 10 )}

n = 1 \sum \infty 6 (- 0.2)^{3 n}

\int \frac{x ^{2}}{9 + x ^{6}} d x

x \to 0 lim (\frac{x ^{3} + 6 x}{x})

\int cos^{2} (a x) d x

n = 7 \sum \infty \frac{1}{( n - 4 ) ^{4}}

What is the derivative of y=ln(1/(xsqrt(x-10))) ?
The derivative of y=ln(1/(xsqrt(x-10))) is -(3x-20)/(2x(x-10))
What is the first derivative of y=ln(1/(xsqrt(x-10))) ?
The first derivative of y=ln(1/(xsqrt(x-10))) is -(3x-20)/(2x(x-10))