What is the derivative of sqrt(1+2x)-sqrt(1-4x) ?

The derivative of sqrt(1+2x)-sqrt(1-4x) is 1/(sqrt(1+2x))+2/(sqrt(1-4x))

What is the first derivative of sqrt(1+2x)-sqrt(1-4x) ?

The first derivative of sqrt(1+2x)-sqrt(1-4x) is 1/(sqrt(1+2x))+2/(sqrt(1-4x))

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\frac{d}{d x} (1 + 2 x - 1 - 4 x)

\frac{1}{1 + 2 x} + \frac{2}{1 - 4 x}

Solution steps

\frac{d}{d x} (1 + 2 x - 1 - 4 x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1 + 2 x) - \frac{d}{d x} (1 - 4 x)

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

\frac{d}{d x} (1 - 4 x) = - \frac{2}{1 - 4 x}

= \frac{1}{1 + 2 x} - (- \frac{2}{1 - 4 x})

Simplify

= \frac{1}{1 + 2 x} + \frac{2}{1 - 4 x}

What is the derivative of sqrt(1+2x)-sqrt(1-4x) ?
The derivative of sqrt(1+2x)-sqrt(1-4x) is 1/(sqrt(1+2x))+2/(sqrt(1-4x))
What is the first derivative of sqrt(1+2x)-sqrt(1-4x) ?
The first derivative of sqrt(1+2x)-sqrt(1-4x) is 1/(sqrt(1+2x))+2/(sqrt(1-4x))