What is (d^3)/(dx^3)(sin(x^3)) ?

The answer to (d^3)/(dx^3)(sin(x^3)) is 3(-9x^6cos(x^3)-18x^3sin(x^3)+2cos(x^3))

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(d^3)/(dx^3)(sin(x^3))

\frac{d ^{3}}{d x ^{3}} (sin (x^{3}))

3 (- 9 x^{6} cos (x^{3}) - 18 x^{3} sin (x^{3}) + 2 cos (x^{3}))

Solution steps

\frac{d ^{3}}{d x ^{3}} (sin (x^{3}))

\frac{d}{d x} (sin (x^{3})) = cos (x^{3}) \cdot 3 x^{2}

= \frac{d ^{2}}{d x ^{2}} (cos (x^{3}) \cdot 3 x^{2})

\frac{d}{d x} (cos (x^{3}) \cdot 3 x^{2}) = 3 (- 3 x^{4} sin (x^{3}) + 2 x cos (x^{3}))

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

\frac{d}{d x} (3 (- 3 x^{4} sin (x^{3}) + 2 x cos (x^{3}))) = 3 (- 9 x^{6} cos (x^{3}) - 18 x^{3} sin (x^{3}) + 2 cos (x^{3}))

= 3 (- 9 x^{6} cos (x^{3}) - 18 x^{3} sin (x^{3}) + 2 cos (x^{3}))

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What is (d^3)/(dx^3)(sin(x^3)) ?
The answer to (d^3)/(dx^3)(sin(x^3)) is 3(-9x^6cos(x^3)-18x^3sin(x^3)+2cos(x^3))