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Popular >

derivative of ln(sqrt(x^2))

Solution

derivative of

ln (x^{2})

Solution

\frac{x}{x ^{2} ∣ x ∣}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{x ^{2}} \cdot \frac{x}{∣ x ∣} : \frac{x}{x ^{2} ∣ x ∣}

= \frac{x}{x ^{2} ∣ x ∣}

Popular Examples

9y^{''}-12y^'+4y=0,y(0)=2,y^'(0)=-1

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

derivative of 3x^5-5x^3-10

\frac{d}{d x} (3 x^{5} - 5 x^{3} - 10)

derivative of (4t-1)(3t-6)^{-1}derivative of

(4 t - 1) (3 t - 6)^{- 1}

y^{''}+4y^'+4y=0,y(-1)=2,y^'(-1)=1

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 1

(\partial)/(\partial y)(8x^{y/z})

\frac{\partial}{\partial y} (8 x^{\frac{y}{z}})

Frequently Asked Questions (FAQ)

What is the derivative of ln(sqrt(x^2)) ?
The derivative of ln(sqrt(x^2)) is x/(sqrt(x^2)|x|)
What is the first derivative of ln(sqrt(x^2)) ?
The first derivative of ln(sqrt(x^2)) is x/(sqrt(x^2)|x|)