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Popular >

derivative of (x^2-2^{-3})

Solution

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

Solution

- \frac{6 x}{( x ^{2} - 2 ) ^{4}}

Solution steps

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

Apply the chain rule:

- \frac{3}{( x ^{2} - 2 ) ^{4}} \frac{d}{d x} (x^{2} - 2)

= - \frac{3}{( x ^{2} - 2 ) ^{4}} \frac{d}{d x} (x^{2} - 2)

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

= - \frac{3}{( x ^{2} - 2 ) ^{4}} \cdot 2 x

Simplify

- \frac{3}{( x ^{2} - 2 ) ^{4}} \cdot 2 x : - \frac{6 x}{( x ^{2} - 2 ) ^{4}}

= - \frac{6 x}{( x ^{2} - 2 ) ^{4}}

Graph

Popular Examples

(\partial)/(\partial x)(1/(2y))

\frac{\partial}{\partial x} (\frac{1}{2 y})

integral of-xe^{-x^2}

\int - x e^{- x^{2}} d x

tangent of f(x)=x^2+x,\at x=-2 tangent of

f (x) = x^{2} + x, at x = - 2

2 x \frac{d y}{d x} = y

limit as x approaches 1/3 of |3x-1|-5

x \to \frac{1}{3} lim (∣ 3 x - 1 ∣ - 5)

Frequently Asked Questions (FAQ)

What is the derivative of (x^2-2^{-3}) ?
The derivative of (x^2-2^{-3}) is -(6x)/((x^2-2)^4)
What is the first derivative of (x^2-2^{-3}) ?
The first derivative of (x^2-2^{-3}) is -(6x)/((x^2-2)^4)