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Popular >

derivative of (1-x^2^{3/2})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of-2x^{-3}*ln(x+x^{-1})

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

limit as x approaches-9 of (x^2-7)/(9-x)

x \to - 9 lim (\frac{x ^{2} - 7}{9 - x})

(\partial)/(\partial x)(4x^2y^3+7xy^2-7x^2)

\frac{\partial}{\partial x} (4 x^{2} y^{3} + 7 x y^{2} - 7 x^{2})

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y = 4 π^{2}

integral of (x^2+3x)^{12}(2x+3)

\int (x^{2} + 3 x)^{12} (2 x + 3) d x

Frequently Asked Questions (FAQ)

What is the derivative of (1-x^2^{3/2}) ?
The derivative of (1-x^2^{3/2}) is -3x(1-x^2)^{1/2}
What is the first derivative of (1-x^2^{3/2}) ?
The first derivative of (1-x^2^{3/2}) is -3x(1-x^2)^{1/2}