What is the d/(dt)(t/(sqrt(t^2+16))) ?

The d/(dt)(t/(sqrt(t^2+16))) is (16)/((t^2+16)sqrt(t^2+16))

What is the first d/(dt)(t/(sqrt(t^2+16))) ?

The first d/(dt)(t/(sqrt(t^2+16))) is (16)/((t^2+16)sqrt(t^2+16))

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\frac{d}{d t} (\frac{t}{t ^{2} + 16})

\frac{16}{( t ^{2} + 16 ) t ^{2} + 16}

Solution steps

\frac{d}{d t} (\frac{t}{t ^{2} + 16})

Apply the Quotient Rule:

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

= \frac{\frac{d t}{d t} t ^{2} + 16 - \frac{d}{d t} ( t ^{2} + 16 ) t}{( t ^{2} + 16 ) ^{2}}

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

\frac{d}{d t} (t^{2} + 16) = \frac{t}{t ^{2} + 16}

= \frac{1 \cdot t ^{2} + 16 - \frac{t}{t ^{2} + 16} t}{( t ^{2} + 16 ) ^{2}}

Simplify

\frac{1 \cdot t ^{2} + 16 - \frac{t}{t ^{2} + 16} t}{( t ^{2} + 16 ) ^{2}} : \frac{16}{( t ^{2} + 16 ) t ^{2} + 16}

= \frac{16}{( t ^{2} + 16 ) t ^{2} + 16}

- x^{3} + x^{2} + 16 x, 4 x

\int \frac{2 x - 3}{x ^{3} + x} d x

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

\int \frac{2 x + 5}{2 x + 6} d x

\frac{d}{d x} (\frac{x ^{3}}{3} + \frac{x ^{2}}{2} + e^{- x})

What is the d/(dt)(t/(sqrt(t^2+16))) ?
The d/(dt)(t/(sqrt(t^2+16))) is (16)/((t^2+16)sqrt(t^2+16))
What is the first d/(dt)(t/(sqrt(t^2+16))) ?
The first d/(dt)(t/(sqrt(t^2+16))) is (16)/((t^2+16)sqrt(t^2+16))