What is the derivative of 1/((1-2500x^4)) ?

The derivative of 1/((1-2500x^4)) is (10000)/((1-2500x)^5)

What is the first derivative of 1/((1-2500x^4)) ?

The first derivative of 1/((1-2500x^4)) is (10000)/((1-2500x)^5)

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\frac{d}{d x} (\frac{1}{( 1 - 2500 x ) ^{4}})

\frac{10000}{( 1 - 2500 x ) ^{5}}

Solution steps

\frac{d}{d x} (\frac{1}{( 1 - 2500 x ) ^{4}})

Apply exponent rule:

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

= \frac{d}{d x} ((1 - 2500 x)^{- 4})

Apply the chain rule:

- \frac{4}{( 1 - 2500 x ) ^{5}} \frac{d}{d x} (1 - 2500 x)

= - \frac{4}{( 1 - 2500 x ) ^{5}} \frac{d}{d x} (1 - 2500 x)

\frac{d}{d x} (1 - 2500 x) = - 2500

= - \frac{4}{( 1 - 2500 x ) ^{5}} (- 2500)

Simplify

- \frac{4}{( 1 - 2500 x ) ^{5}} (- 2500) : \frac{10000}{( 1 - 2500 x ) ^{5}}

= \frac{10000}{( 1 - 2500 x ) ^{5}}

What is the derivative of 1/((1-2500x^4)) ?
The derivative of 1/((1-2500x^4)) is (10000)/((1-2500x)^5)
What is the first derivative of 1/((1-2500x^4)) ?
The first derivative of 1/((1-2500x^4)) is (10000)/((1-2500x)^5)