What is the derivative of-12xcos(x^2+8x^3sin(x^2)) ?

The derivative of-12xcos(x^2+8x^3sin(x^2)) is -12cos(x^2)+48x^2sin(x^2)+16x^4cos(x^2)

What is the first derivative of-12xcos(x^2+8x^3sin(x^2)) ?

The first derivative of-12xcos(x^2+8x^3sin(x^2)) is -12cos(x^2)+48x^2sin(x^2)+16x^4cos(x^2)

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\frac{d}{d x} (- 12 x cos (x^{2}) + 8 x^{3} sin (x^{2}))

- 12 cos (x^{2}) + 48 x^{2} sin (x^{2}) + 16 x^{4} cos (x^{2})

Solution steps

\frac{d}{d x} (- 12 x cos (x^{2}) + 8 x^{3} sin (x^{2}))

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (12 x cos (x^{2})) + \frac{d}{d x} (8 x^{3} sin (x^{2}))

\frac{d}{d x} (12 x cos (x^{2})) = 12 (cos (x^{2}) - 2 x^{2} sin (x^{2}))

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

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

Simplify

- 12 (cos (x^{2}) - 2 x^{2} sin (x^{2})) + 8 (3 x^{2} sin (x^{2}) + 2 x^{4} cos (x^{2})) : - 12 cos (x^{2}) + 48 x^{2} sin (x^{2}) + 16 x^{4} cos (x^{2})

= - 12 cos (x^{2}) + 48 x^{2} sin (x^{2}) + 16 x^{4} cos (x^{2})

\frac{d}{d x} (12 x^{3} - 48 x^{2} + 48 x)

\frac{1}{s ^{2} + 6 s + 13}

\int \frac{x ^{2} + 49}{x} d x

f (x) = x - 4

\frac{d}{d x} (\frac{1}{2 x ^{3}})

What is the derivative of-12xcos(x^2+8x^3sin(x^2)) ?
The derivative of-12xcos(x^2+8x^3sin(x^2)) is -12cos(x^2)+48x^2sin(x^2)+16x^4cos(x^2)
What is the first derivative of-12xcos(x^2+8x^3sin(x^2)) ?
The first derivative of-12xcos(x^2+8x^3sin(x^2)) is -12cos(x^2)+48x^2sin(x^2)+16x^4cos(x^2)