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Popular >

derivative of sqrt(1+2x)-sqrt(1-4x)

Solution

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

Solution

\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}

Popular Examples

integral of 1/(xsqrt(x^2+9))

\int \frac{1}{x x ^{2} + 9} d x

integral of 4/((x+1))

\int \frac{4}{( x + 1 )} d x

(d^2y)/(dt^2)+5(dy)/(dt)+6y=3cos(2t)

\frac{d ^{2} y}{d t ^{2}} + 5 \frac{d y}{d t} + 6 y = 3 cos (2 t)

inverse oflaplace 3/((s+2))inverse laplace

\frac{3}{( s + 2 )}

y^{''}+2y^'+2y=e^{-t}cos(t)

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- t} cos (t)

Frequently Asked Questions (FAQ)

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))