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

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

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

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

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

Solution steps

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

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

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

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

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

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

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

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

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

\int_{- 2}^{2} 2 x^{2} - 2 x d x

\int_{0}^{x} f (t) d t

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

\frac{\partial}{\partial x} (- \frac{2 y}{( 2 x + 3 y ) ^{2}})

y^{^{'}} = 2 y, y (0) = 1

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