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Popular >

derivative of x^3sqrt(1-x^2)

Solution

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

Solution

\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}}

Popular Examples

sum from n=1 to infinity of (n!)/(3n!-1)

n = 1 \sum \infty \frac{n !}{3 n ! - 1}

area y=3x+1,y=13+2x-x^2 area

y = 3 x + 1, y = 13 + 2 x - x^{2}

tangent of f(x)=sqrt(2x+1),\at x=1 tangent of

f (x) = 2 x + 1, at x = 1

derivative of (2x+|x|/(1+|x|))

\frac{d}{d x} (\frac{2 x + ∣ x ∣}{1 + ∣ x ∣})

integral of (9x^2-8x+20)/(x^3+4x)

\int \frac{9 x ^{2} - 8 x + 20}{x ^{3} + 4 x} d x

Frequently Asked Questions (FAQ)

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