What is the derivative of-(19)/((2x-5)^2) ?

The derivative of-(19)/((2x-5)^2) is (76)/((2x-5)^3)

What is the first derivative of-(19)/((2x-5)^2) ?

The first derivative of-(19)/((2x-5)^2) is (76)/((2x-5)^3)

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derivative of

- \frac{19}{( 2 x - 5 ) ^{2}}

\frac{76}{( 2 x - 5 ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{19}{( 2 x - 5 ) ^{2}})

Take the constant out:

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

= - 19 \frac{d}{d x} (\frac{1}{( 2 x - 5 ) ^{2}})

Apply exponent rule:

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

= - 19 \frac{d}{d x} ((2 x - 5)^{- 2})

Apply the chain rule:

- \frac{2}{( 2 x - 5 ) ^{3}} \frac{d}{d x} (2 x - 5)

= - \frac{2}{( 2 x - 5 ) ^{3}} \frac{d}{d x} (2 x - 5)

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

= - 19 (- \frac{2}{( 2 x - 5 ) ^{3}} \cdot 2)

Simplify

- 19 (- \frac{2}{( 2 x - 5 ) ^{3}} \cdot 2) : \frac{76}{( 2 x - 5 ) ^{3}}

= \frac{76}{( 2 x - 5 ) ^{3}}

x \to - 26.8 lim (- 26.8)

\frac{4}{x + 2}, 0

x \to \infty lim (10 \cdot e^{\frac{- x}{2}} + 4)

\frac{d y}{d x} = \frac{4 x}{9 y}

\frac{d}{d x} (e^{- 1 x})

What is the derivative of-(19)/((2x-5)^2) ?
The derivative of-(19)/((2x-5)^2) is (76)/((2x-5)^3)
What is the first derivative of-(19)/((2x-5)^2) ?
The first derivative of-(19)/((2x-5)^2) is (76)/((2x-5)^3)