What is the derivative of (sqrt(x)+2)(x^3-x) ?

The derivative of (sqrt(x)+2)(x^3-x) is (7x^2sqrt(x)+12x^2-3sqrt(x))/2-2

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

The first derivative of (sqrt(x)+2)(x^3-x) is (7x^2sqrt(x)+12x^2-3sqrt(x))/2-2

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derivative

\frac{7 x ^{2} x + 12 x ^{2} - 3 x}{2} - 2

Solution steps

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

Apply the Product Rule:

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

f = x + 2, g = x^{3} - x

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

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

\frac{d}{d x} (x^{3} - x) = 3 x^{2} - 1

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

Simplify

\frac{1}{2 x} (x^{3} - x) + (3 x^{2} - 1) (x + 2) : \frac{7 x ^{2} x + 12 x ^{2} - 3 x}{2} - 2

= \frac{7 x ^{2} x + 12 x ^{2} - 3 x}{2} - 2

What is the derivative of (sqrt(x)+2)(x^3-x) ?
The derivative of (sqrt(x)+2)(x^3-x) is (7x^2sqrt(x)+12x^2-3sqrt(x))/2-2
What is the first derivative of (sqrt(x)+2)(x^3-x) ?
The first derivative of (sqrt(x)+2)(x^3-x) is (7x^2sqrt(x)+12x^2-3sqrt(x))/2-2