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

The derivative of t/(sqrt(t^2+1)) is 1/((t^2+1)sqrt(t^2+1))

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

The first derivative of t/(sqrt(t^2+1)) is 1/((t^2+1)sqrt(t^2+1))

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d t}{d t} = 1

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

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

Simplify

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

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

\int 5 e^{7 x} d x

\int \frac{y + 4}{2} - \frac{y ^{2}}{2} d y

\int \frac{4 ln ( x )}{x} d x

x^{π}

cos (x^{2})

What is the derivative of t/(sqrt(t^2+1)) ?
The derivative of t/(sqrt(t^2+1)) is 1/((t^2+1)sqrt(t^2+1))
What is the first derivative of t/(sqrt(t^2+1)) ?
The first derivative of t/(sqrt(t^2+1)) is 1/((t^2+1)sqrt(t^2+1))