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

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

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

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

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derivative of

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

4 x^{3} + 2 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 4 x^{3} + 2 x

\int e^{6 x + 9} d x

\frac{\partial}{\partial y} (x e^{- x^{2} - y^{2}})

\int_{0}^{4} x 16 - x^{2} d x

\int \frac{1 - t}{t} d t

x \to 1 lim (3 x^{3} - 5 x^{2} + x + 5)

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