What is the derivative of f(t)=sqrt(t/(t^2+7)) ?

The derivative of f(t)=sqrt(t/(t^2+7)) is (-t^2+7)/(2sqrt(t)(t^2+7)^{3/2)}

What is the first derivative of f(t)=sqrt(t/(t^2+7)) ?

The first derivative of f(t)=sqrt(t/(t^2+7)) is (-t^2+7)/(2sqrt(t)(t^2+7)^{3/2)}

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derivative of

f (t) = \frac{t}{t ^{2} + 7}

\frac{- t ^{2} + 7}{2 t ( t ^{2} + 7 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d t} (\frac{t}{t ^{2} + 7})

Apply the chain rule:

\frac{1}{2 \frac{t}{t ^{2} + 7}} \frac{d}{d t} (\frac{t}{t ^{2} + 7})

= \frac{1}{2 \frac{t}{t ^{2} + 7}} \frac{d}{d t} (\frac{t}{t ^{2} + 7})

\frac{d}{d t} (\frac{t}{t ^{2} + 7}) = \frac{- t ^{2} + 7}{( t ^{2} + 7 ) ^{2}}

= \frac{1}{2 \frac{t}{t ^{2} + 7}} \cdot \frac{- t ^{2} + 7}{( t ^{2} + 7 ) ^{2}}

Simplify

\frac{1}{2 \frac{t}{t ^{2} + 7}} \cdot \frac{- t ^{2} + 7}{( t ^{2} + 7 ) ^{2}} : \frac{- t ^{2} + 7}{2 t ( t ^{2} + 7 ) ^{\frac{3}{2}}}

= \frac{- t ^{2} + 7}{2 t ( t ^{2} + 7 ) ^{\frac{3}{2}}}

\int_{1}^{e^{5}} \frac{ln ^{2} ( x ^{2} )}{x} d x

y = 3 x + sin (5 x)

\frac{d}{d x} ((x^{2} - x)^{4})

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

\frac{d}{d x} (a^{2} + x^{2})

What is the derivative of f(t)=sqrt(t/(t^2+7)) ?
The derivative of f(t)=sqrt(t/(t^2+7)) is (-t^2+7)/(2sqrt(t)(t^2+7)^{3/2)}
What is the first derivative of f(t)=sqrt(t/(t^2+7)) ?
The first derivative of f(t)=sqrt(t/(t^2+7)) is (-t^2+7)/(2sqrt(t)(t^2+7)^{3/2)}