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Popular >

derivative of f(x)=xsqrt(1-x^2)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Popular Examples

integral from 0 to 3 of pi(9-x^2)

\int_{0}^{3} π (9 - x^{2}) d x

integral from 0 to x of 3e^{-t^2}

\int_{0}^{x} 3 e^{- t^{2}} d t

derivative of (3+sinh(x)/(1+coth^2(x)))

\frac{d}{d x} (\frac{3 + sinh ( x )}{1 + coth ^{2} ( x )})

derivative of arctan(-5x)

\frac{d}{d x} (arctan (- 5 x))

(\partial)/(\partial y)(2x^2-xy-5x+1)

\frac{\partial}{\partial y} (2 x^{2} - x y - 5 x + 1)

Frequently Asked Questions (FAQ)

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