What is the derivative of f(x)=(4x-2x^3)(4+sqrt(x)) ?

The derivative of f(x)=(4x-2x^3)(4+sqrt(x)) is -24x^2-7x^2sqrt(x)+6sqrt(x)+16

What is the first derivative of f(x)=(4x-2x^3)(4+sqrt(x)) ?

The first derivative of f(x)=(4x-2x^3)(4+sqrt(x)) is -24x^2-7x^2sqrt(x)+6sqrt(x)+16

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derivative of

f (x) = (4 x - 2 x^{3}) (4 + x)

- 24 x^{2} - 7 x^{2} x + 6 x + 16

Solution steps

\frac{d}{d x} ((4 x - 2 x^{3}) (4 + x))

Apply the Product Rule:

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

f = 4 x - 2 x^{3}, g = 4 + x

= \frac{d}{d x} (4 x - 2 x^{3}) (4 + x) + \frac{d}{d x} (4 + x) (4 x - 2 x^{3})

\frac{d}{d x} (4 x - 2 x^{3}) = 4 - 6 x^{2}

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

= (4 - 6 x^{2}) (4 + x) + \frac{1}{2 x} (4 x - 2 x^{3})

Simplify

(4 - 6 x^{2}) (4 + x) + \frac{1}{2 x} (4 x - 2 x^{3}) : - 24 x^{2} - 7 x^{2} x + 6 x + 16

= - 24 x^{2} - 7 x^{2} x + 6 x + 16

s l o p e (- 3, 9), (2, - 1)

\frac{d}{d x} (\frac{1}{x \cdot x})

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\int e^{6 x} sin (6 x) d x

What is the derivative of f(x)=(4x-2x^3)(4+sqrt(x)) ?
The derivative of f(x)=(4x-2x^3)(4+sqrt(x)) is -24x^2-7x^2sqrt(x)+6sqrt(x)+16
What is the first derivative of f(x)=(4x-2x^3)(4+sqrt(x)) ?
The first derivative of f(x)=(4x-2x^3)(4+sqrt(x)) is -24x^2-7x^2sqrt(x)+6sqrt(x)+16