What is the derivative of (x^2+1/(sqrt(x))) ?

The derivative of (x^2+1/(sqrt(x))) is (3x^2-1)/(2xsqrt(x))

What is the first derivative of (x^2+1/(sqrt(x))) ?

The first derivative of (x^2+1/(sqrt(x))) is (3x^2-1)/(2xsqrt(x))

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

\frac{3 x ^{2} - 1}{2 x x}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (9 + 4 x)

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

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

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

(3, 8), (- 7, 7)

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