What is the derivative of (5x^2-3(x^2+x+4)) ?

The derivative of (5x^2-3(x^2+x+4)) is 20x^3+15x^2+34x-3

What is the first derivative of (5x^2-3(x^2+x+4)) ?

The first derivative of (5x^2-3(x^2+x+4)) is 20x^3+15x^2+34x-3

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

20 x^{3} + 15 x^{2} + 34 x - 3

Solution steps

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

Apply the Product Rule:

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

f = 5 x^{2} - 3, g = x^{2} + x + 4

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

\frac{d}{d x} (5 x^{2} - 3) = 10 x

\frac{d}{d x} (x^{2} + x + 4) = 2 x + 1

= 10 x (x^{2} + x + 4) + (2 x + 1) (5 x^{2} - 3)

Simplify

10 x (x^{2} + x + 4) + (2 x + 1) (5 x^{2} - 3) : 20 x^{3} + 15 x^{2} + 34 x - 3

= 20 x^{3} + 15 x^{2} + 34 x - 3

What is the derivative of (5x^2-3(x^2+x+4)) ?
The derivative of (5x^2-3(x^2+x+4)) is 20x^3+15x^2+34x-3
What is the first derivative of (5x^2-3(x^2+x+4)) ?
The first derivative of (5x^2-3(x^2+x+4)) is 20x^3+15x^2+34x-3