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Popular >

derivative of sqrt(x)+3/x+sqrt(5)

Solution

\frac{d}{d x} (x + \frac{3}{x} + 5)

Solution

\frac{x ^{\frac{3}{2}} - 6}{2 x ^{\frac{3}{2}} x}

Solution steps

\frac{d}{d x} (x + \frac{3}{x} + 5)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x) + \frac{d}{d x} (\frac{3}{x}) + \frac{d}{d x} (5)

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

\frac{d}{d x} (\frac{3}{x}) = - \frac{3}{x ^{2}}

\frac{d}{d x} (5) = 0

= \frac{1}{2 x} - \frac{3}{x ^{2}} + 0

Simplify

\frac{1}{2 x} - \frac{3}{x ^{2}} + 0 : \frac{x ^{\frac{3}{2}} - 6}{2 x ^{\frac{3}{2}} x}

= \frac{x ^{\frac{3}{2}} - 6}{2 x ^{\frac{3}{2}} x}

Popular Examples

(\partial)/(\partial x)(tan(x/2))

\frac{\partial}{\partial x} (tan (\frac{x}{2}))

y^{'''}+4y^{''}-35y^'-150y=0

y^{^{'''}} + 4 y^{^{''}} - 35 y^{^{'}} - 150 y = 0

integral of 1/(x^{1/3)(x^{2/3}+4)}

\int \frac{1}{x ^{\frac{1}{3}} ( x ^{\frac{2}{3}} + 4 )} d x

derivative of cos^2(x^2)

\frac{d}{d x} (cos^{2} (x^{2}))

derivative of (9^x-15^{-x}/x)

\frac{d}{d x} (\frac{9 ^{x} - 1 5 ^{- x}}{x})

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)+3/x+sqrt(5) ?
The derivative of sqrt(x)+3/x+sqrt(5) is (x^{3/2}-6)/(2x^{3/2)sqrt(x)}
What is the first derivative of sqrt(x)+3/x+sqrt(5) ?
The first derivative of sqrt(x)+3/x+sqrt(5) is (x^{3/2}-6)/(2x^{3/2)sqrt(x)}