What is (d^6)/(dx^6)(sin(x^2)) ?

The answer to (d^6)/(dx^6)(sin(x^2)) is 2(-32x^6sin(x^2)+240x^4cos(x^2)+360x^2sin(x^2)-60cos(x^2))

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(d^6)/(dx^6)(sin(x^2))

\frac{d ^{6}}{d x ^{6}} (sin (x^{2}))

2 (- 32 x^{6} sin (x^{2}) + 240 x^{4} cos (x^{2}) + 360 x^{2} sin (x^{2}) - 60 cos (x^{2}))

Solution steps

\frac{d ^{6}}{d x ^{6}} (sin (x^{2}))

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

= \frac{d ^{5}}{d x ^{5}} (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 ^{4}}{d x ^{4}} (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 ^{3}}{d x ^{3}} (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}))

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

\frac{d}{d x} (2 (8 x^{4} sin (x^{2}) - 24 x^{2} cos (x^{2}) - 6 sin (x^{2}))) = 2 (16 x^{5} cos (x^{2}) + 80 x^{3} sin (x^{2}) - 60 x cos (x^{2}))

= \frac{d}{d x} (2 (16 x^{5} cos (x^{2}) + 80 x^{3} sin (x^{2}) - 60 x cos (x^{2})))

\frac{d}{d x} (2 (16 x^{5} cos (x^{2}) + 80 x^{3} sin (x^{2}) - 60 x cos (x^{2}))) = 2 (- 32 x^{6} sin (x^{2}) + 240 x^{4} cos (x^{2}) + 360 x^{2} sin (x^{2}) - 60 cos (x^{2}))

= 2 (- 32 x^{6} sin (x^{2}) + 240 x^{4} cos (x^{2}) + 360 x^{2} sin (x^{2}) - 60 cos (x^{2}))

x \to 0 lim (\frac{x}{sin ( 7 x )})

y = 2 x^{2} - x + 1, (1, 2)

x \to 1 lim ((x^{2} + x)^{2})

f (t) = t e^{5 - 2 t}

\frac{d}{d a} (sin (a) cos (a))

What is (d^6)/(dx^6)(sin(x^2)) ?
The answer to (d^6)/(dx^6)(sin(x^2)) is 2(-32x^6sin(x^2)+240x^4cos(x^2)+360x^2sin(x^2)-60cos(x^2))