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Popular >

derivative of f(x)=(x+2)*sqrt(-x)

Solution

derivative of

f (x) = (x + 2) \cdot - x

Solution

\frac{- 3 x - 2}{2 - x}

Solution steps

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

Apply the Product Rule:

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

f = x + 2, g = - x

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

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

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

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

Simplify

1 \cdot - x + (- \frac{1}{2 - x}) (x + 2) : \frac{- 3 x - 2}{2 - x}

= \frac{- 3 x - 2}{2 - x}

Popular Examples

(dy}{dx}=\frac{2y)/x-x^2y^2

\frac{d y}{d x} = \frac{2 y}{x} - x^{2} y^{2}

y^{''}+3y^'+2y= 1/(3+e^x)

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{3 + e ^{x}}

d y - (y - 6)^{2} d x = 0

derivative of sqrt(r)+\sqrt[9]{r}derivative of

limit as x approaches 1 of sqrt(2x^2-x)

x \to 1 lim (2 x^{2} - x)

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x+2)*sqrt(-x) ?
The derivative of f(x)=(x+2)*sqrt(-x) is (-3x-2)/(2sqrt(-x))
What is the first derivative of f(x)=(x+2)*sqrt(-x) ?
The first derivative of f(x)=(x+2)*sqrt(-x) is (-3x-2)/(2sqrt(-x))