What is the derivative of (sqrt(t))/(2t-9) ?

The derivative of (sqrt(t))/(2t-9) is (-2t-9)/(2sqrt(t)(2t-9)^2)

What is the first derivative of (sqrt(t))/(2t-9) ?

The first derivative of (sqrt(t))/(2t-9) is (-2t-9)/(2sqrt(t)(2t-9)^2)

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derivative of

\frac{t}{2 t - 9}

\frac{- 2 t - 9}{2 t ( 2 t - 9 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{t}{2 t - 9})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d t} ( t ) ( 2 t - 9 ) - \frac{d}{d t} ( 2 t - 9 ) t}{( 2 t - 9 ) ^{2}}

\frac{d}{d t} (t) = \frac{1}{2 t}

\frac{d}{d t} (2 t - 9) = 2

= \frac{\frac{1}{2 t} ( 2 t - 9 ) - 2 t}{( 2 t - 9 ) ^{2}}

Simplify

\frac{\frac{1}{2 t} ( 2 t - 9 ) - 2 t}{( 2 t - 9 ) ^{2}} : \frac{- 2 t - 9}{2 t ( 2 t - 9 ) ^{2}}

= \frac{- 2 t - 9}{2 t ( 2 t - 9 ) ^{2}}

(6 x^{2} + 5)^{3}

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

\int sec (3 θ) tan (3 θ) d θ

3 t

\frac{\partial}{\partial y} (- x e^{x y})

What is the derivative of (sqrt(t))/(2t-9) ?
The derivative of (sqrt(t))/(2t-9) is (-2t-9)/(2sqrt(t)(2t-9)^2)
What is the first derivative of (sqrt(t))/(2t-9) ?
The first derivative of (sqrt(t))/(2t-9) is (-2t-9)/(2sqrt(t)(2t-9)^2)