What is the derivative of (5x^2-7(3x^2-2x+1)) ?

The derivative of (5x^2-7(3x^2-2x+1)) is 60x^3-30x^2-32x+14

What is the first derivative of (5x^2-7(3x^2-2x+1)) ?

The first derivative of (5x^2-7(3x^2-2x+1)) is 60x^3-30x^2-32x+14

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\frac{d}{d x} ((5 x^{2} - 7) (3 x^{2} - 2 x + 1))

60 x^{3} - 30 x^{2} - 32 x + 14

Solution steps

\frac{d}{d x} ((5 x^{2} - 7) (3 x^{2} - 2 x + 1))

Apply the Product Rule:

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

f = 5 x^{2} - 7, g = 3 x^{2} - 2 x + 1

= \frac{d}{d x} (5 x^{2} - 7) (3 x^{2} - 2 x + 1) + \frac{d}{d x} (3 x^{2} - 2 x + 1) (5 x^{2} - 7)

\frac{d}{d x} (5 x^{2} - 7) = 10 x

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

= 10 x (3 x^{2} - 2 x + 1) + (6 x - 2) (5 x^{2} - 7)

Simplify

10 x (3 x^{2} - 2 x + 1) + (6 x - 2) (5 x^{2} - 7) : 60 x^{3} - 30 x^{2} - 32 x + 14

= 60 x^{3} - 30 x^{2} - 32 x + 14

What is the derivative of (5x^2-7(3x^2-2x+1)) ?
The derivative of (5x^2-7(3x^2-2x+1)) is 60x^3-30x^2-32x+14
What is the first derivative of (5x^2-7(3x^2-2x+1)) ?
The first derivative of (5x^2-7(3x^2-2x+1)) is 60x^3-30x^2-32x+14