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Popular >

derivative of 9sqrt(x)-7/x

Solution

derivative of

9 x - \frac{7}{x}

Solution

\frac{9 x ^{\frac{3}{2}} + 14}{2 x ^{\frac{3}{2}} x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (9 x) = \frac{9}{2 x}

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

= \frac{9}{2 x} - (- \frac{7}{x ^{2}})

Simplify

\frac{9}{2 x} - (- \frac{7}{x ^{2}}) : \frac{9 x ^{\frac{3}{2}} + 14}{2 x ^{\frac{3}{2}} x}

= \frac{9 x ^{\frac{3}{2}} + 14}{2 x ^{\frac{3}{2}} x}

Popular Examples

limit as x approaches-9 of 1/((x+9)^2)

x \to - 9 lim (\frac{1}{( x + 9 ) ^{2}})

integral of cos^3(3x)sin^{-2}(3x)

\int cos^{3} (3 x) sin^{- 2} (3 x) d x

limit as x approaches-infinity of 19

x \to - \infty lim (19)

limit as x approaches 5 of 9

x \to 5 lim (9)

tangent of f(x)=x-x^2,\at x=-1 tangent of

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

Frequently Asked Questions (FAQ)

What is the derivative of 9sqrt(x)-7/x ?
The derivative of 9sqrt(x)-7/x is (9x^{3/2}+14)/(2x^{3/2)sqrt(x)}
What is the first derivative of 9sqrt(x)-7/x ?
The first derivative of 9sqrt(x)-7/x is (9x^{3/2}+14)/(2x^{3/2)sqrt(x)}