What is (d^6)/(dx^6)(sqrt(1-x^2)) ?

The answer to (d^6)/(dx^6)(sqrt(1-x^2)) is -(45(8x^4+12x^2+1))/((1-x^2)^{11/2)}

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(d^6)/(dx^6)(sqrt(1-x^2))

\frac{d ^{6}}{d x ^{6}} (1 - x^{2})

- \frac{45 ( 8 x ^{4} + 12 x ^{2} + 1 )}{( 1 - x ^{2} ) ^{\frac{11}{2}}}

Solution steps

\frac{d ^{6}}{d x ^{6}} (1 - x^{2})

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

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

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

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

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

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

\frac{d}{d x} (- \frac{3 x}{( 1 - x ^{2} ) ^{\frac{5}{2}}}) = - \frac{3 ( 4 x ^{2} + 1 )}{( 1 - x ^{2} ) ^{\frac{7}{2}}}

= \frac{d ^{2}}{d x ^{2}} (- \frac{3 ( 4 x ^{2} + 1 )}{( 1 - x ^{2} ) ^{\frac{7}{2}}})

\frac{d}{d x} (- \frac{3 ( 4 x ^{2} + 1 )}{( 1 - x ^{2} ) ^{\frac{7}{2}}}) = - \frac{15 x ( 4 x ^{2} + 3 )}{( 1 - x ^{2} ) ^{\frac{9}{2}}}

= \frac{d}{d x} (- \frac{15 x ( 4 x ^{2} + 3 )}{( 1 - x ^{2} ) ^{\frac{9}{2}}})

\frac{d}{d x} (- \frac{15 x ( 4 x ^{2} + 3 )}{( 1 - x ^{2} ) ^{\frac{9}{2}}}) = - \frac{45 ( 8 x ^{4} + 12 x ^{2} + 1 )}{( 1 - x ^{2} ) ^{\frac{11}{2}}}

= - \frac{45 ( 8 x ^{4} + 12 x ^{2} + 1 )}{( 1 - x ^{2} ) ^{\frac{11}{2}}}

\int \frac{27}{1 + 9 x ^{2}} d x

y^{^{''}} - 8 y^{^{'}} + 3 y = x e^{x}

\frac{d}{d x} (cos (h) (x))

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

\frac{d}{d x} ((x^{3} - x) e^{x})

What is (d^6)/(dx^6)(sqrt(1-x^2)) ?
The answer to (d^6)/(dx^6)(sqrt(1-x^2)) is -(45(8x^4+12x^2+1))/((1-x^2)^{11/2)}