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Popular >

derivative of pi/((2x^5))

Solution

\frac{d}{d x} (\frac{π}{( 2 x ) ^{5}})

Solution

- \frac{5 π}{32 x ^{6}}

Solution steps

\frac{d}{d x} (\frac{π}{( 2 x ) ^{5}})

Take the constant out:

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

= π \frac{d}{d x} (\frac{1}{( 2 x ) ^{5}})

Apply exponent rule:

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

= π \frac{d}{d x} ((2 x)^{- 5})

Apply the chain rule:

- \frac{5}{( 2 x ) ^{6}} \frac{d}{d x} (2 x)

= - \frac{5}{( 2 x ) ^{6}} \frac{d}{d x} (2 x)

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

= π (- \frac{5}{( 2 x ) ^{6}} \cdot 2)

Simplify

π (- \frac{5}{( 2 x ) ^{6}} \cdot 2) : - \frac{5 π}{32 x ^{6}}

= - \frac{5 π}{32 x ^{6}}

Popular Examples

derivative of y=(x^2-4x+3)/(x^2)derivative of

y = \frac{x ^{2} - 4 x + 3}{x ^{2}}

integral from 1 to 2 of 1/(2x-1)

\int_{1}^{2} \frac{1}{2 x - 1} d x

integral of sqrt(27-x^2)

\int 27 - x^{2} d x

limit as x approaches pi/2 of e^{tan(x)}

x \to \frac{π}{2} lim (e^{t a n (x)})

derivative of y=(4x)/(x^2+1)derivative of

y = \frac{4 x}{x ^{2} + 1}

Frequently Asked Questions (FAQ)

What is the derivative of pi/((2x^5)) ?
The derivative of pi/((2x^5)) is -(5pi)/(32x^6)
What is the first derivative of pi/((2x^5)) ?
The first derivative of pi/((2x^5)) is -(5pi)/(32x^6)