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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\frac{d}{d x} (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}

\frac{\partial}{\partial x} (8 x^{2} y + 5 x y^{3})

y = 7 x^{2} - 4 x, - 74

\int (x - 9)^{2} d x

\int_{0}^{\frac{π}{3}} tan^{5} (x) d x

y^{^{''}} + \frac{6}{x} y^{^{'}} + \frac{4}{x ^{2}} y = 0

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