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Popular >

derivative of x(x^2+1^2)

Solution

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

Solution

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

Solution steps

\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}

= \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)

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

Simplify

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

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

Popular Examples

integral from 0 to 1 of (4x+6)/((x+1)^2)

\int_{0}^{1} \frac{4 x + 6}{( x + 1 ) ^{2}} d x

derivative of-x^3+2x^2-x

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

integral of (3x^2-2)/(x^3-2x-8)

\int \frac{3 x ^{2} - 2}{x ^{3} - 2 x - 8} d x

limit as t approaches 3+of ln(t-3)

t \to 3 + lim (ln (t - 3))

limit as x approaches-pi/4 of csc(x)

x \to - \frac{π}{4} lim (csc (x))

Frequently Asked Questions (FAQ)

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