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

The derivative of (2x+sqrt(x)(x^2-x)) is (x^{3/2}-3sqrt(x)+12x^2-8x+4xsqrt(x))/2

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

The first derivative of (2x+sqrt(x)(x^2-x)) is (x^{3/2}-3sqrt(x)+12x^2-8x+4xsqrt(x))/2

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

\frac{x ^{\frac{3}{2}} - 3 x + 12 x ^{2} - 8 x + 4 x x}{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(2 + \frac{1}{2 x}) (x^{2} - x) + (2 x - 1) (2 x + x) : \frac{x ^{\frac{3}{2}} - 3 x + 12 x ^{2} - 8 x + 4 x x}{2}

= \frac{x ^{\frac{3}{2}} - 3 x + 12 x ^{2} - 8 x + 4 x x}{2}

sec^{2} (θ)

\frac{d}{d x} (\frac{cos ( x )}{x ^{6}})

\frac{1}{2 - x}

\int (1 + x + e^{x}) d x

f (z) = tan (e^{- 6 z})

What is the derivative of (2x+sqrt(x)(x^2-x)) ?
The derivative of (2x+sqrt(x)(x^2-x)) is (x^{3/2}-3sqrt(x)+12x^2-8x+4xsqrt(x))/2
What is the first derivative of (2x+sqrt(x)(x^2-x)) ?
The first derivative of (2x+sqrt(x)(x^2-x)) is (x^{3/2}-3sqrt(x)+12x^2-8x+4xsqrt(x))/2