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Popular >

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

Solution

derivative of

f (x) = 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

derivative of y=((x^2+3)/(x^2-3))^8 derivative of

y = (\frac{x ^{2} + 3}{x ^{2} - 3})^{8}

derivative of f(x)= 7/(1-x)derivative of

f (x) = \frac{7}{1 - x}

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

x^{2} x^{3} + 1

limit as x approaches 8 of x

x \to 8 lim (x)

integral of y^3(4y^2-25)

\int y^{3} (4 y^{2} - 25) d y

Frequently Asked Questions (FAQ)

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