What is the derivative of 7sqrt(x)-9/(x^6) ?

The derivative of 7sqrt(x)-9/(x^6) is (7x^{13/2}+108)/(2x^{13/2)sqrt(x)}

What is the first derivative of 7sqrt(x)-9/(x^6) ?

The first derivative of 7sqrt(x)-9/(x^6) is (7x^{13/2}+108)/(2x^{13/2)sqrt(x)}

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derivative of

7 x - \frac{9}{x ^{6}}

\frac{7 x ^{\frac{13}{2}} + 108}{2 x ^{\frac{13}{2}} x}

Solution steps

\frac{d}{d x} (7 x - \frac{9}{x ^{6}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (7 x) - \frac{d}{d x} (\frac{9}{x ^{6}})

\frac{d}{d x} (7 x) = \frac{7}{2 x}

\frac{d}{d x} (\frac{9}{x ^{6}}) = - \frac{54}{x ^{7}}

= \frac{7}{2 x} - (- \frac{54}{x ^{7}})

Simplify

\frac{7}{2 x} - (- \frac{54}{x ^{7}}) : \frac{7 x ^{\frac{13}{2}} + 108}{2 x ^{\frac{13}{2}} x}

= \frac{7 x ^{\frac{13}{2}} + 108}{2 x ^{\frac{13}{2}} x}

f (x) = x e^{- \frac{x}{2}}, at x = \frac{1}{2}

\int \frac{x ^{3}}{x ^{4} - 1} d x

t^{2} y^{^{''}} + 2 t y^{^{'}} - 30 y = 0

x \to 3 lim (\frac{( x + 3 )}{x - 3})

\int (ln (5 x))^{2} d x

What is the derivative of 7sqrt(x)-9/(x^6) ?
The derivative of 7sqrt(x)-9/(x^6) is (7x^{13/2}+108)/(2x^{13/2)sqrt(x)}
What is the first derivative of 7sqrt(x)-9/(x^6) ?
The first derivative of 7sqrt(x)-9/(x^6) is (7x^{13/2}+108)/(2x^{13/2)sqrt(x)}