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

The derivative of f(x)=-sqrt(1-x)x^2 is -(-5x^2+4x)/(2sqrt(1-x))

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

The first derivative of f(x)=-sqrt(1-x)x^2 is -(-5x^2+4x)/(2sqrt(1-x))

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derivative of

f (x) = - 1 - x x^{2}

- \frac{- 5 x ^{2} + 4 x}{2 1 - x}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

- ((- \frac{1}{2 1 - x}) x^{2} + 2 x 1 - x) : - \frac{- 5 x ^{2} + 4 x}{2 1 - x}

= - \frac{- 5 x ^{2} + 4 x}{2 1 - x}

What is the derivative of f(x)=-sqrt(1-x)x^2 ?
The derivative of f(x)=-sqrt(1-x)x^2 is -(-5x^2+4x)/(2sqrt(1-x))
What is the first derivative of f(x)=-sqrt(1-x)x^2 ?
The first derivative of f(x)=-sqrt(1-x)x^2 is -(-5x^2+4x)/(2sqrt(1-x))