What is the derivative of (5t-2)/(3t+1) ?

The derivative of (5t-2)/(3t+1) is (11)/((3t+1)^2)

What is the first derivative of (5t-2)/(3t+1) ?

The first derivative of (5t-2)/(3t+1) is (11)/((3t+1)^2)

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derivative of

\frac{5 t - 2}{3 t + 1}

\frac{11}{( 3 t + 1 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{5 t - 2}{3 t + 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d t} ( 5 t - 2 ) ( 3 t + 1 ) - \frac{d}{d t} ( 3 t + 1 ) ( 5 t - 2 )}{( 3 t + 1 ) ^{2}}

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

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

= \frac{5 ( 3 t + 1 ) - 3 ( 5 t - 2 )}{( 3 t + 1 ) ^{2}}

Expand

5 (3 t + 1) - 3 (5 t - 2) : 11

= \frac{11}{( 3 t + 1 ) ^{2}}

\int [x ln (x^{2} + 1) + (x^{2} + 1) y] d x

8 9 x^{2} + 5

\frac{\partial}{\partial y} (9 - x^{2} - 3 y)

\frac{\partial}{\partial x} (2 sin (6 x) cos (4 y))

y = \frac{x}{5} - 4

What is the derivative of (5t-2)/(3t+1) ?
The derivative of (5t-2)/(3t+1) is (11)/((3t+1)^2)
What is the first derivative of (5t-2)/(3t+1) ?
The first derivative of (5t-2)/(3t+1) is (11)/((3t+1)^2)