What is the derivative of-6/((x+1^4)) ?

The derivative of-6/((x+1^4)) is (24)/((x+1)^5)

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

The first derivative of-6/((x+1^4)) is (24)/((x+1)^5)

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\frac{d}{d x} (- \frac{6}{( x + 1 ) ^{4}})

\frac{24}{( x + 1 ) ^{5}}

Solution steps

\frac{d}{d x} (- \frac{6}{( x + 1 ) ^{4}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 6 \frac{d}{d x} (\frac{1}{( x + 1 ) ^{4}})

Apply exponent rule:

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

= - 6 \frac{d}{d x} ((x + 1)^{- 4})

Apply the chain rule:

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

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

\frac{d}{d x} (x + 1) = 1

= - 6 (- \frac{4}{( x + 1 ) ^{5}} \cdot 1)

Simplify

- 6 (- \frac{4}{( x + 1 ) ^{5}} \cdot 1) : \frac{24}{( x + 1 ) ^{5}}

= \frac{24}{( x + 1 ) ^{5}}

x \to \infty lim (x \cdot \frac{x}{x})

\frac{d}{d t} (\frac{3 t ^{2} - 3}{2 t})

\frac{d}{d x} (x^{2} + 2 x + 6)

\int_{0}^{1} \frac{27}{4 y - 1} d y

\frac{d ^{2}}{d x ^{2}} (sin (9 x^{2}))

What is the derivative of-6/((x+1^4)) ?
The derivative of-6/((x+1^4)) is (24)/((x+1)^5)
What is the first derivative of-6/((x+1^4)) ?
The first derivative of-6/((x+1^4)) is (24)/((x+1)^5)