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

The derivative of (2x^2-x-1sqrt(x)) is (10x^2-3x-1)/(2sqrt(x))

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

The first derivative of (2x^2-x-1sqrt(x)) is (10x^2-3x-1)/(2sqrt(x))

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

\frac{10 x ^{2} - 3 x - 1}{2 x}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 x^{2} - x - 1, g = x

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

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

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

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

Simplify

(4 x - 1) x + \frac{1}{2 x} (2 x^{2} - x - 1) : \frac{10 x ^{2} - 3 x - 1}{2 x}

= \frac{10 x ^{2} - 3 x - 1}{2 x}

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

e^{x} - 7 x^{6}

cot (6 - u)

x \to 0 lim (x^{2} + x)

\int (\frac{6}{5})^{x} d x

What is the derivative of (2x^2-x-1sqrt(x)) ?
The derivative of (2x^2-x-1sqrt(x)) is (10x^2-3x-1)/(2sqrt(x))
What is the first derivative of (2x^2-x-1sqrt(x)) ?
The first derivative of (2x^2-x-1sqrt(x)) is (10x^2-3x-1)/(2sqrt(x))