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

The derivative of (x^2+3(x^2-4x)) is 4x^3-12x^2+6x-12

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

The first derivative of (x^2+3(x^2-4x)) is 4x^3-12x^2+6x-12

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

4 x^{3} - 12 x^{2} + 6 x - 12

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x (x^{2} - 4 x) + (2 x - 4) (x^{2} + 3) : 4 x^{3} - 12 x^{2} + 6 x - 12

= 4 x^{3} - 12 x^{2} + 6 x - 12

n = 0 \sum \infty 2 \cdot 0. 3^{n}

\frac{d y}{d x} + x (y^{2} + y) = 0

\int \frac{2 tan ( x )}{1 - tan ^{2} ( x )} d x

\frac{d}{d x} (tan (2 x + 1))

y = x^{3} + 6 x

What is the derivative of (x^2+3(x^2-4x)) ?
The derivative of (x^2+3(x^2-4x)) is 4x^3-12x^2+6x-12
What is the first derivative of (x^2+3(x^2-4x)) ?
The first derivative of (x^2+3(x^2-4x)) is 4x^3-12x^2+6x-12