What is the derivative of pi/((2x^4)) ?

The derivative of pi/((2x^4)) is -pi/(4x^5)

What is the first derivative of pi/((2x^4)) ?

The first derivative of pi/((2x^4)) is -pi/(4x^5)

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\frac{d}{d x} (\frac{π}{( 2 x ) ^{4}})

- \frac{π}{4 x ^{5}}

Solution steps

\frac{d}{d x} (\frac{π}{( 2 x ) ^{4}})

Take the constant out:

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

= π \frac{d}{d x} (\frac{1}{( 2 x ) ^{4}})

Apply exponent rule:

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

= π \frac{d}{d x} ((2 x)^{- 4})

Apply the chain rule:

- \frac{4}{( 2 x ) ^{5}} \frac{d}{d x} (2 x)

= - \frac{4}{( 2 x ) ^{5}} \frac{d}{d x} (2 x)

\frac{d}{d x} (2 x) = 2

= π (- \frac{4}{( 2 x ) ^{5}} \cdot 2)

Simplify

π (- \frac{4}{( 2 x ) ^{5}} \cdot 2) : - \frac{π}{4 x ^{5}}

= - \frac{π}{4 x ^{5}}

\frac{d y}{d x} = 2 x y - 6 x

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

f (x) = (7 x + 1)^{2}

6^{x}

\int 8 x^{17} e^{- x^{9}} d x

What is the derivative of pi/((2x^4)) ?
The derivative of pi/((2x^4)) is -pi/(4x^5)
What is the first derivative of pi/((2x^4)) ?
The first derivative of pi/((2x^4)) is -pi/(4x^5)