What is the derivative of (-4x^5-2pi^2/(x^7)) ?

The derivative of (-4x^5-2pi^2/(x^7)) is -(2(-4x^5-7pi^2))/(x^8)

What is the first derivative of (-4x^5-2pi^2/(x^7)) ?

The first derivative of (-4x^5-2pi^2/(x^7)) is -(2(-4x^5-7pi^2))/(x^8)

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\frac{d}{d x} (\frac{- 4 x ^{5} - 2 π ^{2}}{x ^{7}})

- \frac{2 ( - 4 x ^{5} - 7 π ^{2} )}{x ^{8}}

Solution steps

\frac{d}{d x} (\frac{- 4 x ^{5} - 2 π ^{2}}{x ^{7}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( - 4 x ^{5} - 2 π ^{2} ) x ^{7} - \frac{d}{d x} ( x ^{7} ) ( - 4 x ^{5} - 2 π ^{2} )}{( x ^{7} ) ^{2}}

\frac{d}{d x} (- 4 x^{5} - 2 π^{2}) = - 20 x^{4}

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{( - 20 x ^{4} ) x ^{7} - 7 x ^{6} ( - 4 x ^{5} - 2 π ^{2} )}{( x ^{7} ) ^{2}}

Simplify

\frac{( - 20 x ^{4} ) x ^{7} - 7 x ^{6} ( - 4 x ^{5} - 2 π ^{2} )}{( x ^{7} ) ^{2}} : - \frac{2 ( - 4 x ^{5} - 7 π ^{2} )}{x ^{8}}

= - \frac{2 ( - 4 x ^{5} - 7 π ^{2} )}{x ^{8}}

What is the derivative of (-4x^5-2pi^2/(x^7)) ?
The derivative of (-4x^5-2pi^2/(x^7)) is -(2(-4x^5-7pi^2))/(x^8)
What is the first derivative of (-4x^5-2pi^2/(x^7)) ?
The first derivative of (-4x^5-2pi^2/(x^7)) is -(2(-4x^5-7pi^2))/(x^8)