What is the derivative of 6x(x^2+1)^2 ?

The derivative of 6x(x^2+1)^2 is 6(5x^4+6x^2+1)

What is the first derivative of 6x(x^2+1)^2 ?

The first derivative of 6x(x^2+1)^2 is 6(5x^4+6x^2+1)

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derivative of

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

6 (5 x^{4} + 6 x^{2} + 1)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 6 (1 \cdot (x^{2} + 1)^{2} + 4 x (x^{2} + 1) x)

Simplify

6 (1 \cdot (x^{2} + 1)^{2} + 4 x (x^{2} + 1) x) : 6 (5 x^{4} + 6 x^{2} + 1)

= 6 (5 x^{4} + 6 x^{2} + 1)

x^{^{'}}

1 - 5, 2 x^{2} + 11, 0

\int 31 sec^{- 2} (x t a) n^{3} x d x

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

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

What is the derivative of 6x(x^2+1)^2 ?
The derivative of 6x(x^2+1)^2 is 6(5x^4+6x^2+1)
What is the first derivative of 6x(x^2+1)^2 ?
The first derivative of 6x(x^2+1)^2 is 6(5x^4+6x^2+1)