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Popular >

derivative of (1-2x)^{1/2}

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of 1/((x+1)sqrt(x^2+2x-3))

\int \frac{1}{( x + 1 ) x ^{2} + 2 x - 3} d x

integral of ((1+cos(2x))/2)^2

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

derivative of cos(ln(t))derivative of

cos (ln (t))

x(dy)/(dx)+4y=x^{-3}e^x

x \frac{d y}{d x} + 4 y = x^{- 3} e^{x}

integral of x/2

\int \frac{x}{2} d x

Frequently Asked Questions (FAQ)

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