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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{1}{1 + 5 x ^{2}} d x

\int 4 sin^{3} (x co) s^{2} x d x

y = x + 225, (0, 15)

\int 2 x^{2} - 2 d x

\frac{d}{d x} (\frac{1 - x ^{2}}{x})

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