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Popular >

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

Solution

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

Solution

2 x

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= 2 x

Popular Examples

integral of (x+1)^{10}

\int (x + 1)^{10} d x

sin(2x)dx+cos(4y)dy=0,y(pi/2)= pi/4

sin (2 x) d x + cos (4 y) d y = 0, y (\frac{π}{2}) = \frac{π}{4}

tangent of y=2x+3cos(x)tangent of

y = 2 x + 3 cos (x)

limit as x approaches 0 of f(x)

x \to 0 lim (f (x))

(\partial)/(\partial x)((4+5y)^x)

\frac{\partial}{\partial x} ((4 + 5 y)^{x})

Frequently Asked Questions (FAQ)

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