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

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

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

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

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\frac{d}{d 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

\int \frac{5 x ^{2} + 7}{x \frac{4}{3}} d x

x \to 0 lim (sin (\frac{π}{2} - x))

\frac{d}{d x} (lo g_{l n (x)} (e))

\int \frac{3}{x} d x

x \to 0 lim (\frac{x ^{3} - 1}{x - 1})

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