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Popular >

derivative of f(x)=-sqrt(x)

Solution

derivative of

f (x) = - x

Solution

- \frac{1}{2 x}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply the Power Rule:

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

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

Simplify

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

= - \frac{1}{2 x}

Popular Examples

taylor ln(x/2),2 taylor

ln (\frac{x}{2}), 2

integral from 0 to 2 of 1/((x^2+4)^2)

\int_{0}^{2} \frac{1}{( x ^{2} + 4 ) ^{2}} d x

integral of (x^2-3x+2)

\int (x^{2} - 3 x + 2) d x

integral of 1/(x-\sqrt[3]{x)}

limit as x approaches 0 of x^2*e^{1/x}

x \to 0 lim (x^{2} \cdot e^{\frac{1}{x}})

Frequently Asked Questions (FAQ)

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