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Popular >

derivative of 9sqrt(x)-1/x

Solution

\frac{d}{d x} (9 x - \frac{1}{x})

Solution

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

Solution steps

\frac{d}{d x} (9 x - \frac{1}{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (9 x) - \frac{d}{d x} (\frac{1}{x})

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

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

= \frac{9}{2 x} - (- \frac{1}{x ^{2}})

Simplify

\frac{9}{2 x} - (- \frac{1}{x ^{2}}) : \frac{9 x ^{\frac{3}{2}} + 2}{2 x ^{\frac{3}{2}} x}

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

Popular Examples

derivative of f(x)=4x^5ln(x)derivative of

f (x) = 4 x^{5} ln (x)

laplacetransform e^{20t}laplace transform

e^{20 t}

y^'=((xy^2))/((1+x^2))

y^{^{'}} = \frac{( x y ^{2} )}{( 1 + x ^{2} )}

y^{''}-16y^'+64y=0,y(0)=1,y(1)=0

y^{^{''}} - 16 y^{^{'}} + 64 y = 0, y (0) = 1, y (1) = 0

limit as x approaches 0 of (1-2x)^{3/x}

x \to 0 lim ((1 - 2 x)^{\frac{3}{x}})

Frequently Asked Questions (FAQ)

What is the derivative of 9sqrt(x)-1/x ?
The derivative of 9sqrt(x)-1/x is (9x^{3/2}+2)/(2x^{3/2)sqrt(x)}
What is the first derivative of 9sqrt(x)-1/x ?
The first derivative of 9sqrt(x)-1/x is (9x^{3/2}+2)/(2x^{3/2)sqrt(x)}