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Popular >

derivative of sqrt(x-x^2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)(e^{3x^2y}(1+x-2y))

\frac{\partial}{\partial x} (e^{3 x^{2} y} (1 + x - 2 y))

derivative of sqrt(9-4x)

\frac{d}{d x} (9 - 4 x)

integral of pi(x+1)^2

\int π (x + 1)^{2} d x

limit as (x,y) approaches (0,9) of x^3y

(x, y) \to (0, 9) lim (x^{3} y)

(\partial)/(\partial x)(e^{x*cos(y)})

\frac{\partial}{\partial x} (e^{x \cdot c o s (y)})

Frequently Asked Questions (FAQ)

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