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Popular >

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

Solution

derivative of

x (1 - x^{2})

Solution

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

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 2 of xsqrt(x^2-4)

x \to 2 lim (x x^{2} - 4)

y^{''}+5y^'+y=0

y^{^{''}} + 5 y^{^{'}} + y = 0

integral of ((6x^2+4))/((3y^2-4))

\int \frac{( 6 x ^{2} + 4 )}{( 3 y ^{2} - 4 )}

(\partial)/(\partial x)(4x^8y^6+5x^7y^5)

\frac{\partial}{\partial x} (4 x^{8} y^{6} + 5 x^{7} y^{5})

integral from-infinity to 8 of e^{0.04x}

\int_{- \infty}^{8} e^{0.04 x} d x

Frequently Asked Questions (FAQ)

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