What is the derivative of f(x)=(x^2-5x+8)(3x^2-2) ?

The derivative of f(x)=(x^2-5x+8)(3x^2-2) is 12x^3-45x^2+44x+10

What is the first derivative of f(x)=(x^2-5x+8)(3x^2-2) ?

The first derivative of f(x)=(x^2-5x+8)(3x^2-2) is 12x^3-45x^2+44x+10

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derivative of

f (x) = (x^{2} - 5 x + 8) (3 x^{2} - 2)

12 x^{3} - 45 x^{2} + 44 x + 10

Solution steps

\frac{d}{d x} ((x^{2} - 5 x + 8) (3 x^{2} - 2))

Apply the Product Rule:

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

f = x^{2} - 5 x + 8, g = 3 x^{2} - 2

= \frac{d}{d x} (x^{2} - 5 x + 8) (3 x^{2} - 2) + \frac{d}{d x} (3 x^{2} - 2) (x^{2} - 5 x + 8)

\frac{d}{d x} (x^{2} - 5 x + 8) = 2 x - 5

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

= (2 x - 5) (3 x^{2} - 2) + 6 x (x^{2} - 5 x + 8)

Simplify

(2 x - 5) (3 x^{2} - 2) + 6 x (x^{2} - 5 x + 8) : 12 x^{3} - 45 x^{2} + 44 x + 10

= 12 x^{3} - 45 x^{2} + 44 x + 10

\frac{d}{d x} (\frac{1}{x + y})

\int 6 x + 12 x ln (8 x) d x

\int (x^{- 2}) d x

(10 y^{2} - x y) d x + x^{2} d y = 0

x \to \infty lim (6 x^{2})

What is the derivative of f(x)=(x^2-5x+8)(3x^2-2) ?
The derivative of f(x)=(x^2-5x+8)(3x^2-2) is 12x^3-45x^2+44x+10
What is the first derivative of f(x)=(x^2-5x+8)(3x^2-2) ?
The first derivative of f(x)=(x^2-5x+8)(3x^2-2) is 12x^3-45x^2+44x+10