What is the derivative of t/(sqrt(t^2+36)) ?

The derivative of t/(sqrt(t^2+36)) is (36)/((t^2+36)sqrt(t^2+36))

What is the first derivative of t/(sqrt(t^2+36)) ?

The first derivative of t/(sqrt(t^2+36)) is (36)/((t^2+36)sqrt(t^2+36))

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derivative of

\frac{t}{t ^{2} + 36}

\frac{36}{( t ^{2} + 36 ) t ^{2} + 36}

Solution steps

\frac{d}{d t} (\frac{t}{t ^{2} + 36})

Apply the Quotient Rule:

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

= \frac{\frac{d t}{d t} t ^{2} + 36 - \frac{d}{d t} ( t ^{2} + 36 ) t}{( t ^{2} + 36 ) ^{2}}

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

\frac{d}{d t} (t^{2} + 36) = \frac{t}{t ^{2} + 36}

= \frac{1 \cdot t ^{2} + 36 - \frac{t}{t ^{2} + 36} t}{( t ^{2} + 36 ) ^{2}}

Simplify

\frac{1 \cdot t ^{2} + 36 - \frac{t}{t ^{2} + 36} t}{( t ^{2} + 36 ) ^{2}} : \frac{36}{( t ^{2} + 36 ) t ^{2} + 36}

= \frac{36}{( t ^{2} + 36 ) t ^{2} + 36}

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\int_{0}^{4} \frac{1}{4 - x} d x

d er i v a t i v e \frac{2 x ^{3} + 8}{x}

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What is the derivative of t/(sqrt(t^2+36)) ?
The derivative of t/(sqrt(t^2+36)) is (36)/((t^2+36)sqrt(t^2+36))
What is the first derivative of t/(sqrt(t^2+36)) ?
The first derivative of t/(sqrt(t^2+36)) is (36)/((t^2+36)sqrt(t^2+36))