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Popular >

derivative of (-4+x^2^{-1})

Solution

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

Solution

- \frac{2 x}{( - 4 + x ^{2} ) ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of (sqrt(x)/2-2/(sqrt(x)))

\frac{d}{d x} (\frac{x}{2} - \frac{2}{x})

integral of (x+pi)cos(nx)

\int (x + π) cos (n x) d x

y^{''}+2*y^'+y=6*x*e^{-x}

y^{^{''}} + 2 \cdot y^{^{'}} + y = 6 \cdot x \cdot e^{- x}

integral of tan^2(4x)sec^4(4x)

\int tan^{2} (4 x) sec^{4} (4 x) d x

tangent of 2sqrt(x)(1.2)tangent of

2 x (1.2)

Frequently Asked Questions (FAQ)

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