What is the derivative of 1/((t^5+4)^4) ?

The derivative of 1/((t^5+4)^4) is -(20t^4)/((t^5+4)^5)

What is the first derivative of 1/((t^5+4)^4) ?

The first derivative of 1/((t^5+4)^4) is -(20t^4)/((t^5+4)^5)

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derivative of

\frac{1}{( t ^{5} + 4 ) ^{4}}

- \frac{20 t ^{4}}{( t ^{5} + 4 ) ^{5}}

Solution steps

\frac{d}{d t} (\frac{1}{( t ^{5} + 4 ) ^{4}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d t} ((t^{5} + 4)^{- 4})

Apply the chain rule:

- \frac{4}{( t ^{5} + 4 ) ^{5}} \frac{d}{d t} (t^{5} + 4)

= - \frac{4}{( t ^{5} + 4 ) ^{5}} \frac{d}{d t} (t^{5} + 4)

\frac{d}{d t} (t^{5} + 4) = 5 t^{4}

= - \frac{4}{( t ^{5} + 4 ) ^{5}} \cdot 5 t^{4}

Simplify

- \frac{4}{( t ^{5} + 4 ) ^{5}} \cdot 5 t^{4} : - \frac{20 t ^{4}}{( t ^{5} + 4 ) ^{5}}

= - \frac{20 t ^{4}}{( t ^{5} + 4 ) ^{5}}

\frac{d}{d x} (- ln (x - 2))

\int \frac{( x ^{2} - x + 8 )}{x ^{3} + 2 x} d x

6 t (\frac{d y}{d t}) + 5 y = t

\frac{\partial}{\partial w} (\frac{w}{h ( w ) ^{2}})

y = \frac{1}{6 x - 1}

What is the derivative of 1/((t^5+4)^4) ?
The derivative of 1/((t^5+4)^4) is -(20t^4)/((t^5+4)^5)
What is the first derivative of 1/((t^5+4)^4) ?
The first derivative of 1/((t^5+4)^4) is -(20t^4)/((t^5+4)^5)