What is the derivative of (4x^3+5x(x-3)(x+5)) ?

The derivative of (4x^3+5x(x-3)(x+5)) is 20x^4+32x^3-165x^2+20x-75

What is the first derivative of (4x^3+5x(x-3)(x+5)) ?

The first derivative of (4x^3+5x(x-3)(x+5)) is 20x^4+32x^3-165x^2+20x-75

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\frac{d}{d x} ((4 x^{3} + 5 x) (x - 3) (x + 5))

20 x^{4} + 32 x^{3} - 165 x^{2} + 20 x - 75

Solution steps

\frac{d}{d x} ((4 x^{3} + 5 x) (x - 3) (x + 5))

Apply the Product Rule:

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

f = 4 x^{3} + 5 x, g = (x - 3) (x + 5)

= \frac{d}{d x} (4 x^{3} + 5 x) (x - 3) (x + 5) + \frac{d}{d x} ((x - 3) (x + 5)) (4 x^{3} + 5 x)

\frac{d}{d x} (4 x^{3} + 5 x) = 12 x^{2} + 5

\frac{d}{d x} ((x - 3) (x + 5)) = 2 x + 2

= (12 x^{2} + 5) (x - 3) (x + 5) + (2 x + 2) (4 x^{3} + 5 x)

Simplify

(12 x^{2} + 5) (x - 3) (x + 5) + (2 x + 2) (4 x^{3} + 5 x) : 20 x^{4} + 32 x^{3} - 165 x^{2} + 20 x - 75

= 20 x^{4} + 32 x^{3} - 165 x^{2} + 20 x - 75

\frac{d}{d x} (5 arcsin (3) x^{3})

\frac{1}{11 x}

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

x \to 1 lim ([f (x) + 5 g (x)])

x + y \frac{d y}{d x} = x - y

What is the derivative of (4x^3+5x(x-3)(x+5)) ?
The derivative of (4x^3+5x(x-3)(x+5)) is 20x^4+32x^3-165x^2+20x-75
What is the first derivative of (4x^3+5x(x-3)(x+5)) ?
The first derivative of (4x^3+5x(x-3)(x+5)) is 20x^4+32x^3-165x^2+20x-75