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

The derivative of (2x^2+1/(sqrt(x))) is (6x^2-1)/(2xsqrt(x))

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

The first derivative of (2x^2+1/(sqrt(x))) is (6x^2-1)/(2xsqrt(x))

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

\frac{6 x ^{2} - 1}{2 x x}

Solution steps

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

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

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

= \frac{4 x x - \frac{1}{2 x} ( 2 x ^{2} + 1 )}{( x ) ^{2}}

Simplify

\frac{4 x x - \frac{1}{2 x} ( 2 x ^{2} + 1 )}{( x ) ^{2}} : \frac{6 x ^{2} - 1}{2 x x}

= \frac{6 x ^{2} - 1}{2 x x}

\int 6 e^{4 t a n (2 x)} sec^{2} (2 x) d x

\frac{d}{d x} (\frac{- x ^{2}}{y ^{2}})

\int \frac{x}{1 + 2 x} d x

\int (3 x zy + x y^{2} + 2 z x^{2}) d x

x \to 3 + lim (f (x))

What is the derivative of (2x^2+1/(sqrt(x))) ?
The derivative of (2x^2+1/(sqrt(x))) is (6x^2-1)/(2xsqrt(x))
What is the first derivative of (2x^2+1/(sqrt(x))) ?
The first derivative of (2x^2+1/(sqrt(x))) is (6x^2-1)/(2xsqrt(x))