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

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

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

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

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

\frac{1}{x ^{5}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

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

= \frac{1}{x ^{5}}

\int cos (x) sin (x) d x

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

f (x) = cos (x^{2}) \cdot 2 x

\int \frac{15}{16 + r ^{2}} d r

6 e^{- 4 t} + 5 e^{- 5 t} + 4 t e^{- 6 t}

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