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

The derivative of (2x+1^2(x^2+x+1)) is 4(2x+1)(x^2+x+1)+(2x+1)^3

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

The first derivative of (2x+1^2(x^2+x+1)) is 4(2x+1)(x^2+x+1)+(2x+1)^3

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

4 (2 x + 1) (x^{2} + x + 1) + (2 x + 1)^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

(2 x + 1) (2 x + 1)^{2} = (2 x + 1)^{3}

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

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

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

\int θ sin (θ) d θ

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

ln (ln (3 x))

What is the derivative of (2x+1^2(x^2+x+1)) ?
The derivative of (2x+1^2(x^2+x+1)) is 4(2x+1)(x^2+x+1)+(2x+1)^3
What is the first derivative of (2x+1^2(x^2+x+1)) ?
The first derivative of (2x+1^2(x^2+x+1)) is 4(2x+1)(x^2+x+1)+(2x+1)^3