What is the derivative of 2cos(x^2-4x^2sin(x^2)) ?

The derivative of 2cos(x^2-4x^2sin(x^2)) is -12xsin(x^2)-8x^3cos(x^2)

What is the first derivative of 2cos(x^2-4x^2sin(x^2)) ?

The first derivative of 2cos(x^2-4x^2sin(x^2)) is -12xsin(x^2)-8x^3cos(x^2)

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

- 12 x sin (x^{2}) - 8 x^{3} cos (x^{2})

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

- 4 x sin (x^{2}) - 4 (2 x sin (x^{2}) + 2 x^{3} cos (x^{2})) : - 12 x sin (x^{2}) - 8 x^{3} cos (x^{2})

= - 12 x sin (x^{2}) - 8 x^{3} cos (x^{2})

What is the derivative of 2cos(x^2-4x^2sin(x^2)) ?
The derivative of 2cos(x^2-4x^2sin(x^2)) is -12xsin(x^2)-8x^3cos(x^2)
What is the first derivative of 2cos(x^2-4x^2sin(x^2)) ?
The first derivative of 2cos(x^2-4x^2sin(x^2)) is -12xsin(x^2)-8x^3cos(x^2)