What is the derivative of f(x)=(x^3-3x)(2x^2+3x+5) ?

The derivative of f(x)=(x^3-3x)(2x^2+3x+5) is 10x^4+12x^3-3x^2-18x-15

What is the first derivative of f(x)=(x^3-3x)(2x^2+3x+5) ?

The first derivative of f(x)=(x^3-3x)(2x^2+3x+5) is 10x^4+12x^3-3x^2-18x-15

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derivative of

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

10 x^{4} + 12 x^{3} - 3 x^{2} - 18 x - 15

Solution steps

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

Apply the Product Rule:

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

f = x^{3} - 3 x, g = 2 x^{2} + 3 x + 5

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

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

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

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

Simplify

(3 x^{2} - 3) (2 x^{2} + 3 x + 5) + (4 x + 3) (x^{3} - 3 x) : 10 x^{4} + 12 x^{3} - 3 x^{2} - 18 x - 15

= 10 x^{4} + 12 x^{3} - 3 x^{2} - 18 x - 15

\int 2 sin (θ) - sec^{2} (θ) d θ

x \to + 0 lim (\frac{x}{arctan ( x )})

\int_{- 1}^{1} 3 e^{- 3 x} d x

5 e^{- 2 t}

y^{^{'}} = 12 t^{5} - 20 t^{4} + 2 - 6 t^{- 2}

What is the derivative of f(x)=(x^3-3x)(2x^2+3x+5) ?
The derivative of f(x)=(x^3-3x)(2x^2+3x+5) is 10x^4+12x^3-3x^2-18x-15
What is the first derivative of f(x)=(x^3-3x)(2x^2+3x+5) ?
The first derivative of f(x)=(x^3-3x)(2x^2+3x+5) is 10x^4+12x^3-3x^2-18x-15