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

The derivative of (3sqrt(x)+x(2-x^2)) is -3x^2-6xsqrt(x)-(3x^{3/2})/2+3/(sqrt(x))+2

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

The first derivative of (3sqrt(x)+x(2-x^2)) is -3x^2-6xsqrt(x)-(3x^{3/2})/2+3/(sqrt(x))+2

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

- 3 x^{2} - 6 x x - \frac{3 x ^{\frac{3}{2}}}{2} + \frac{3}{x} + 2

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(\frac{3}{2 x} + 1) (2 - x^{2}) + (- 2 x) (3 x + x) : - 3 x^{2} - 6 x x - \frac{3 x ^{\frac{3}{2}}}{2} + \frac{3}{x} + 2

= - 3 x^{2} - 6 x x - \frac{3 x ^{\frac{3}{2}}}{2} + \frac{3}{x} + 2

\int_{1}^{6} 8 x d x

\frac{5 x}{1 + x ^{2}}

\frac{\partial}{\partial x} (x y + x)

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

\int (cos (x) - sec (x)) d x

What is the derivative of (3sqrt(x)+x(2-x^2)) ?
The derivative of (3sqrt(x)+x(2-x^2)) is -3x^2-6xsqrt(x)-(3x^{3/2})/2+3/(sqrt(x))+2
What is the first derivative of (3sqrt(x)+x(2-x^2)) ?
The first derivative of (3sqrt(x)+x(2-x^2)) is -3x^2-6xsqrt(x)-(3x^{3/2})/2+3/(sqrt(x))+2