What is the derivative of f(x)=x^3sqrt(1-x^2) ?

The derivative of f(x)=x^3sqrt(1-x^2) is (-4x^4+3x^2)/(sqrt(1-x^2))

What is the first derivative of f(x)=x^3sqrt(1-x^2) ?

The first derivative of f(x)=x^3sqrt(1-x^2) is (-4x^4+3x^2)/(sqrt(1-x^2))

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derivative of

f (x) = x^{3} 1 - x^{2}

\frac{- 4 x ^{4} + 3 x ^{2}}{1 - x ^{2}}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = 1 - x^{2}

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

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

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

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

Simplify

3 x^{2} 1 - x^{2} + (- \frac{x}{1 - x ^{2}}) x^{3} : \frac{- 4 x ^{4} + 3 x ^{2}}{1 - x ^{2}}

= \frac{- 4 x ^{4} + 3 x ^{2}}{1 - x ^{2}}

y = 1 + x, y = \frac{( x + 3 )}{3}

\int sec^{3} (9 x) d x

f (x) = (ln (x))^{3}, at x = 3

\int \frac{( 5 x + 1 )}{( 2 x + 1 ) ( x - 1 )} d x

y^{^{''''}} + 3 y^{^{''}} - 4 y = 0

What is the derivative of f(x)=x^3sqrt(1-x^2) ?
The derivative of f(x)=x^3sqrt(1-x^2) is (-4x^4+3x^2)/(sqrt(1-x^2))
What is the first derivative of f(x)=x^3sqrt(1-x^2) ?
The first derivative of f(x)=x^3sqrt(1-x^2) is (-4x^4+3x^2)/(sqrt(1-x^2))