What is the derivative of (t(t(2t+1)^2)) ?

The derivative of (t(t(2t+1)^2)) is 16x^3+12x^2+2x

What is the first derivative of (t(t(2t+1)^2)) ?

The first derivative of (t(t(2t+1)^2)) is 16x^3+12x^2+2x

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

16 x^{3} + 12 x^{2} + 2 x

Solution steps

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

Simplify

(x) (x (2 x + 1)^{2}) : x^{2} (2 x + 1)^{2}

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

Apply the Product Rule:

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

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

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

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

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

= 2 x (2 x + 1)^{2} + 4 (2 x + 1) x^{2}

Simplify

2 x (2 x + 1)^{2} + 4 (2 x + 1) x^{2} : 16 x^{3} + 12 x^{2} + 2 x

= 16 x^{3} + 12 x^{2} + 2 x

24 (x - \frac{1}{6})

- (2 x + 1) cos (5)

\frac{1}{( n + 1 ) \cdot ( n + 2 )}

- (2 x + 1) cos (2)

\frac{3 w ^{2} - 5 w + 14}{( 4 w + 8 ) ( w + 2 )}

What is the derivative of (t(t(2t+1)^2)) ?
The derivative of (t(t(2t+1)^2)) is 16x^3+12x^2+2x
What is the first derivative of (t(t(2t+1)^2)) ?
The first derivative of (t(t(2t+1)^2)) is 16x^3+12x^2+2x