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

The derivative of x^2sqrt(1-x^2) is (-3x^3+2x)/(sqrt(1-x^2))

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

The first derivative of x^2sqrt(1-x^2) is (-3x^3+2x)/(sqrt(1-x^2))

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

\frac{- 3 x ^{3} + 2 x}{1 - x ^{2}}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = 1 - x^{2}

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

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

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

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

Simplify

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

= \frac{- 3 x ^{3} + 2 x}{1 - x ^{2}}

\frac{d}{d x} (- 8 ln (x))

y = 7 x^{- 7}

(3 x + 2 y + 2 y^{2}) d x + (x + 2 x y) d y = 0

\frac{d}{d t} (k^{2} sin^{2} (t))

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