What is the derivative of (3t-1)/(sqrt(t)-2) ?

The derivative of (3t-1)/(sqrt(t)-2) is (3t-12sqrt(t)+1)/(2sqrt(t)(\sqrt{t)-2)^2}

What is the first derivative of (3t-1)/(sqrt(t)-2) ?

The first derivative of (3t-1)/(sqrt(t)-2) is (3t-12sqrt(t)+1)/(2sqrt(t)(\sqrt{t)-2)^2}

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derivative of

\frac{3 t - 1}{t - 2}

\frac{3 t - 12 t + 1}{2 t ( t - 2 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{3 t - 1}{t - 2})

Apply the Quotient Rule:

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

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

\frac{d}{d t} (3 t - 1) = 3

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

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

Simplify

\frac{3 ( t - 2 ) - \frac{1}{2 t} ( 3 t - 1 )}{( t - 2 ) ^{2}} : \frac{3 t - 12 t + 1}{2 t ( t - 2 ) ^{2}}

= \frac{3 t - 12 t + 1}{2 t ( t - 2 ) ^{2}}

\frac{\partial}{\partial x} (\frac{x}{2 y})

\int \frac{2}{cos ( x )} e^{2 l n (c o s (x))} d x

\int_{1}^{x} \frac{2}{x ^{3}} d x

y = \frac{x - 1}{x + 1}

\frac{d}{d x} (7 x^{- 6} - 5 x^{- 3})

What is the derivative of (3t-1)/(sqrt(t)-2) ?
The derivative of (3t-1)/(sqrt(t)-2) is (3t-12sqrt(t)+1)/(2sqrt(t)(\sqrt{t)-2)^2}
What is the first derivative of (3t-1)/(sqrt(t)-2) ?
The first derivative of (3t-1)/(sqrt(t)-2) is (3t-12sqrt(t)+1)/(2sqrt(t)(\sqrt{t)-2)^2}