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

The derivative of x(x^2+1)^3 is (x^2+1)^3+6x^2(x^2+1)^2

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

The first derivative of x(x^2+1)^3 is (x^2+1)^3+6x^2(x^2+1)^2

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derivative of

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

(x^{2} + 1)^{3} + 6 x^{2} (x^{2} + 1)^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot (x^{2} + 1)^{3} + 6 x (x^{2} + 1)^{2} x : (x^{2} + 1)^{3} + 6 x^{2} (x^{2} + 1)^{2}

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

f (x) = x^{4} - 4 x^{2}, at x = 1

\int 25 - y^{2} d y

3 x - 6, - 2 x + 10, 2, 5

\frac{d y}{d x} + x y = 0

\int \frac{x}{x ^{2} - 5 x + 6} d x

What is the derivative of x(x^2+1)^3 ?
The derivative of x(x^2+1)^3 is (x^2+1)^3+6x^2(x^2+1)^2
What is the first derivative of x(x^2+1)^3 ?
The first derivative of x(x^2+1)^3 is (x^2+1)^3+6x^2(x^2+1)^2