What is (d^4)/(dx^4)(sin(x^2)) ?

The answer to (d^4)/(dx^4)(sin(x^2)) is 2(8x^4sin(x^2)-24x^2cos(x^2)-6sin(x^2))

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(d^4)/(dx^4)(sin(x^2))

\frac{d ^{4}}{d x ^{4}} (sin (x^{2}))

2 (8 x^{4} sin (x^{2}) - 24 x^{2} cos (x^{2}) - 6 sin (x^{2}))

Solution steps

\frac{d ^{4}}{d x ^{4}} (sin (x^{2}))

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

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

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

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

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

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

\frac{d}{d x} (2 (- 4 x^{3} cos (x^{2}) - 6 x sin (x^{2}))) = 2 (8 x^{4} sin (x^{2}) - 24 x^{2} cos (x^{2}) - 6 sin (x^{2}))

= 2 (8 x^{4} sin (x^{2}) - 24 x^{2} cos (x^{2}) - 6 sin (x^{2}))

What is (d^4)/(dx^4)(sin(x^2)) ?
The answer to (d^4)/(dx^4)(sin(x^2)) is 2(8x^4sin(x^2)-24x^2cos(x^2)-6sin(x^2))