What is the derivative of (sqrt(t))/(2t+3) ?

The derivative of (sqrt(t))/(2t+3) is (-2t+3)/(2sqrt(t)(2t+3)^2)

What is the first derivative of (sqrt(t))/(2t+3) ?

The first derivative of (sqrt(t))/(2t+3) is (-2t+3)/(2sqrt(t)(2t+3)^2)

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derivative of

\frac{t}{2 t + 3}

\frac{- 2 t + 3}{2 t ( 2 t + 3 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{t}{2 t + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d t} ( t ) ( 2 t + 3 ) - \frac{d}{d t} ( 2 t + 3 ) t}{( 2 t + 3 ) ^{2}}

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

\frac{d}{d t} (2 t + 3) = 2

= \frac{\frac{1}{2 t} ( 2 t + 3 ) - 2 t}{( 2 t + 3 ) ^{2}}

Simplify

\frac{\frac{1}{2 t} ( 2 t + 3 ) - 2 t}{( 2 t + 3 ) ^{2}} : \frac{- 2 t + 3}{2 t ( 2 t + 3 ) ^{2}}

= \frac{- 2 t + 3}{2 t ( 2 t + 3 ) ^{2}}

\int cos^{3} (4 θ) sin (4 θ) d θ

\frac{d y}{d x} = - x e^{- x + y}

y^{^{'}} = y (2 + y) t

\frac{d}{d x} (sin^{x} (x))

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

What is the derivative of (sqrt(t))/(2t+3) ?
The derivative of (sqrt(t))/(2t+3) is (-2t+3)/(2sqrt(t)(2t+3)^2)
What is the first derivative of (sqrt(t))/(2t+3) ?
The first derivative of (sqrt(t))/(2t+3) is (-2t+3)/(2sqrt(t)(2t+3)^2)