(d^3)/(dx^3)(sqrt(2x+3))

解答

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

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

求解步骤

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

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

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

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

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

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

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

\int_{0}^{7} \frac{1}{( 49 + x ^{2} )} d x

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y^{^{'''}} + 8 y^{^{''}} + 52 y^{^{'}} = 0

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