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Popular >

derivative of 2ln(1+x^2)

Solution

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

Solution

\frac{4 x}{1 + x ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= 2 \cdot \frac{1}{1 + x ^{2}} \cdot 2 x

Simplify

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

= \frac{4 x}{1 + x ^{2}}

Popular Examples

(\partial)/(\partial x)(ln(x^3+y^3))

\frac{\partial}{\partial x} (ln (x^{3} + y^{3}))

(\partial}{\partial x}(B(\frac{G(B,x))/a)^{1/x})

\frac{\partial}{\partial x} (B (\frac{G ( B , x )}{a})^{\frac{1}{x}})

(\partial)/(\partial x)(-2x^3+sin(xy)+4e^{4y})

\frac{\partial}{\partial x} (- 2 x^{3} + sin (x y) + 4 e^{4 y})

limit as x approaches 0 of |x|ln|x|

x \to 0 lim (∣ x ∣ ln ∣ x ∣)

inverse oflaplace 1/(s^2)(1-e^{-s})inverse laplace

\frac{1}{s ^{2}} (1 - e^{- s})

Frequently Asked Questions (FAQ)

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