What is the derivative of 3/((4x-5)) ?

The derivative of 3/((4x-5)) is -(12)/((4x-5)^2)

What is the first derivative of 3/((4x-5)) ?

The first derivative of 3/((4x-5)) is -(12)/((4x-5)^2)

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\frac{d}{d x} (\frac{3}{( 4 x - 5 )})

- \frac{12}{( 4 x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3}{( 4 x - 5 )})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{1}{4 x - 5})

Apply exponent rule:

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

= 3 \frac{d}{d x} ((4 x - 5)^{- 1})

Apply the chain rule:

- \frac{1}{( 4 x - 5 ) ^{2}} \frac{d}{d x} (4 x - 5)

= - \frac{1}{( 4 x - 5 ) ^{2}} \frac{d}{d x} (4 x - 5)

\frac{d}{d x} (4 x - 5) = 4

= 3 (- \frac{1}{( 4 x - 5 ) ^{2}} \cdot 4)

Simplify

3 (- \frac{1}{( 4 x - 5 ) ^{2}} \cdot 4) : - \frac{12}{( 4 x - 5 ) ^{2}}

= - \frac{12}{( 4 x - 5 ) ^{2}}

\int 2 x (x^{2} - 1)^{102} d x

\int \frac{2}{1 - x ^{2}} d x

\int - sin^{2} (t) d t

y^{^{'}} + sin (t) y + sin (t) = 0, y (0) = 6

y^{^{''}} + 25 y = 40 sin (5 x)

What is the derivative of 3/((4x-5)) ?
The derivative of 3/((4x-5)) is -(12)/((4x-5)^2)
What is the first derivative of 3/((4x-5)) ?
The first derivative of 3/((4x-5)) is -(12)/((4x-5)^2)