What is the derivative of 8/(x-5) ?

The derivative of 8/(x-5) is -8/((x-5)^2)

What is the first derivative of 8/(x-5) ?

The first derivative of 8/(x-5) is -8/((x-5)^2)

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\frac{d}{d x} (\frac{8}{x - 5})

- \frac{8}{( x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8}{x - 5})

Take the constant out:

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

= 8 \frac{d}{d x} (\frac{1}{x - 5})

Apply exponent rule:

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

= 8 \frac{d}{d x} ((x - 5)^{- 1})

Apply the chain rule:

- \frac{1}{( x - 5 ) ^{2}} \frac{d}{d x} (x - 5)

= - \frac{1}{( x - 5 ) ^{2}} \frac{d}{d x} (x - 5)

\frac{d}{d x} (x - 5) = 1

= 8 (- \frac{1}{( x - 5 ) ^{2}} \cdot 1)

Simplify

8 (- \frac{1}{( x - 5 ) ^{2}} \cdot 1) : - \frac{8}{( x - 5 ) ^{2}}

= - \frac{8}{( x - 5 ) ^{2}}

f (x) = - csc^{2} (x)

(x^{2} - y^{2}) d x + (2 x y) d y = 0

\int \frac{1}{- x ^{2} + 4 x - 3} d x

\int \frac{15}{4} x^{2} d x

\frac{d}{d t} (lo g_{3} (2 t - x))

What is the derivative of 8/(x-5) ?
The derivative of 8/(x-5) is -8/((x-5)^2)
What is the first derivative of 8/(x-5) ?
The first derivative of 8/(x-5) is -8/((x-5)^2)