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

The derivative of 1/((x^4+5^5)) is -(20x^3)/((x^4+5)^6)

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

The first derivative of 1/((x^4+5^5)) is -(20x^3)/((x^4+5)^6)

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

- \frac{20 x ^{3}}{( x ^{4} + 5 ) ^{6}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{5}{( x ^{4} + 5 ) ^{6}} \frac{d}{d x} (x^{4} + 5)

= - \frac{5}{( x ^{4} + 5 ) ^{6}} \frac{d}{d x} (x^{4} + 5)

\frac{d}{d x} (x^{4} + 5) = 4 x^{3}

= - \frac{5}{( x ^{4} + 5 ) ^{6}} \cdot 4 x^{3}

Simplify

- \frac{5}{( x ^{4} + 5 ) ^{6}} \cdot 4 x^{3} : - \frac{20 x ^{3}}{( x ^{4} + 5 ) ^{6}}

= - \frac{20 x ^{3}}{( x ^{4} + 5 ) ^{6}}

\int x^{2} cos (6 x) d x

\int 5 - 4 x d x

\frac{\partial}{\partial x} ((x^{2} + x - y)^{7})

\frac{d}{d x} (x^{3} + 7 x)

\int_{0}^{1} \frac{1}{1 + x ^{2}} d x

What is the derivative of 1/((x^4+5^5)) ?
The derivative of 1/((x^4+5^5)) is -(20x^3)/((x^4+5)^6)
What is the first derivative of 1/((x^4+5^5)) ?
The first derivative of 1/((x^4+5^5)) is -(20x^3)/((x^4+5)^6)