What is the derivative of 1+t/(45t^2+30t) ?

The derivative of 1+t/(45t^2+30t) is -1/(5(3t+2)^2)

What is the first derivative of 1+t/(45t^2+30t) ?

The first derivative of 1+t/(45t^2+30t) is -1/(5(3t+2)^2)

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derivative of

1 + \frac{t}{45 t ^{2} + 30 t}

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

Solution steps

\frac{d}{d t} (1 + \frac{t}{45 t ^{2} + 30 t})

Simplify

1 + \frac{t}{45 t ^{2} + 30 t} : 1 + \frac{1}{15 ( 3 t + 2 )}

= \frac{d}{d t} (1 + \frac{1}{15 ( 3 t + 2 )})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (1) + \frac{d}{d t} (\frac{1}{15 ( 3 t + 2 )})

\frac{d}{d t} (1) = 0

\frac{d}{d t} (\frac{1}{15 ( 3 t + 2 )}) = - \frac{1}{5 ( 3 t + 2 ) ^{2}}

= 0 - \frac{1}{5 ( 3 t + 2 ) ^{2}}

Simplify

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

\frac{d}{d x} (\frac{1}{6} ln ∣ 3 sec (2 x) - 2 ∣ + C)

\int_{0}^{\infty} \frac{1}{x + 1} d x

n = 0 \sum \infty (- 2)^{3 - 2 n} 3

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

\frac{d y}{d x} = y - x, y (0) = \frac{2}{3}

What is the derivative of 1+t/(45t^2+30t) ?
The derivative of 1+t/(45t^2+30t) is -1/(5(3t+2)^2)
What is the first derivative of 1+t/(45t^2+30t) ?
The first derivative of 1+t/(45t^2+30t) is -1/(5(3t+2)^2)