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

The derivative of (2-2x^2(3x+1)^2) is 144x^3-144x^2-16x+16

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

The first derivative of (2-2x^2(3x+1)^2) is 144x^3-144x^2-16x+16

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

144 x^{3} - 144 x^{2} - 16 x + 16

Solution steps

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

Apply the Product Rule:

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

f = (2 - 2 x)^{2}, g = (3 x + 1)^{2}

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

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

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

= (- 4 (2 - 2 x)) (3 x + 1)^{2} + 6 (3 x + 1) (2 - 2 x)^{2}

Simplify

(- 4 (2 - 2 x)) (3 x + 1)^{2} + 6 (3 x + 1) (2 - 2 x)^{2} : 144 x^{3} - 144 x^{2} - 16 x + 16

= 144 x^{3} - 144 x^{2} - 16 x + 16

\frac{d}{d x} (\frac{a + b x}{c + d x})

3 t e^{- 2 t}

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

\int \frac{1}{sin ^{4} ( x )} d x

\frac{d}{d x} (z (x) + x^{2})

What is the derivative of (2-2x^2(3x+1)^2) ?
The derivative of (2-2x^2(3x+1)^2) is 144x^3-144x^2-16x+16
What is the first derivative of (2-2x^2(3x+1)^2) ?
The first derivative of (2-2x^2(3x+1)^2) is 144x^3-144x^2-16x+16