What is (d^3)/(dx^3)(sqrt(1+x)) ?

The answer to (d^3)/(dx^3)(sqrt(1+x)) is 3/(8(1+x)^{5/2)}

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(d^3)/(dx^3)(sqrt(1+x))

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

\frac{3}{8 ( 1 + x ) ^{\frac{5}{2}}}

Solution steps

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

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

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

\frac{d}{d x} (\frac{1}{2 1 + x}) = - \frac{1}{4 ( 1 + x ) ^{\frac{3}{2}}}

= \frac{d}{d x} (- \frac{1}{4 ( 1 + x ) ^{\frac{3}{2}}})

\frac{d}{d x} (- \frac{1}{4 ( 1 + x ) ^{\frac{3}{2}}}) = \frac{3}{8 ( 1 + x ) ^{\frac{5}{2}}}

= \frac{3}{8 ( 1 + x ) ^{\frac{5}{2}}}

\frac{d y}{d x} = 12

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

f (x) = x (x + 3)

\frac{d}{d x} (6 - 3 x)

y^{^{'}} = 3 y + 7, y (0) = 4

What is (d^3)/(dx^3)(sqrt(1+x)) ?
The answer to (d^3)/(dx^3)(sqrt(1+x)) is 3/(8(1+x)^{5/2)}