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Popular >

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

Solution

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

Solution

- \frac{1}{x ^{2}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{1}{2 ( x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2})

= - \frac{1}{2 ( x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2})

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

= - \frac{1}{2 ( x ^{2} ) ^{\frac{3}{2}}} \cdot 2 x

Simplify

- \frac{1}{2 ( x ^{2} ) ^{\frac{3}{2}}} \cdot 2 x : - \frac{1}{x ^{2}}

= - \frac{1}{x ^{2}}

Popular Examples

integral of 2/(1+x^4)

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

derivative of 1/(sqrt(6x))derivative of

\frac{1}{6 x}

integral of e^{ty}(4y+1)

\int e^{t y} (4 y + 1) d y

integral of e^{2x}*sin(x)

\int e^{2 x} \cdot sin (x) d x

tangent of f(x)= 1/6 x^4,\at x=-1 tangent of

f (x) = \frac{1}{6} x^{4}, at x = - 1

Frequently Asked Questions (FAQ)

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