What is the derivative of 13.375ln(x/(x-1250)) ?

The derivative of 13.375ln(x/(x-1250)) is -(16718.75)/(x(x-1250))

What is the first derivative of 13.375ln(x/(x-1250)) ?

The first derivative of 13.375ln(x/(x-1250)) is -(16718.75)/(x(x-1250))

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derivative of

13.375 ln (\frac{x}{x - 1250})

- \frac{16718.75}{x ( x - 1250 )}

Solution steps

\frac{d}{d x} (13.375 ln (\frac{x}{x - 1250}))

Take the constant out:

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

= 13.375 \frac{d}{d x} (ln (\frac{x}{x - 1250}))

Apply the chain rule:

\frac{1}{\frac{x}{x - 1250}} \frac{d}{d x} (\frac{x}{x - 1250})

= \frac{1}{\frac{x}{x - 1250}} \frac{d}{d x} (\frac{x}{x - 1250})

\frac{d}{d x} (\frac{x}{x - 1250}) = - \frac{1250}{( x - 1250 ) ^{2}}

= 13.375 \cdot \frac{1}{\frac{x}{x - 1250}} (- \frac{1250}{( x - 1250 ) ^{2}})

Simplify

13.375 \cdot \frac{1}{\frac{x}{x - 1250}} (- \frac{1250}{( x - 1250 ) ^{2}}) : - \frac{16718.75}{x ( x - 1250 )}

= - \frac{16718.75}{x ( x - 1250 )}

\int 6 x (1 - x) d x

t^{2} \cdot y^{^{'}} + t y = 7, y (1) = 7

\int 8 sin^{2} (x) cos (x) d x

y^{^{''}} + 2 y^{^{'}} + y = 3 x + 8

\frac{d}{d x} (a cos (2 x) + b cos (2 x))

What is the derivative of 13.375ln(x/(x-1250)) ?
The derivative of 13.375ln(x/(x-1250)) is -(16718.75)/(x(x-1250))
What is the first derivative of 13.375ln(x/(x-1250)) ?
The first derivative of 13.375ln(x/(x-1250)) is -(16718.75)/(x(x-1250))