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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derivative of

- 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} (arccos (\frac{10}{x}))

\frac{x}{x + \frac{c}{x}}

f (x) = e^{x} - 6 x^{5}

5 sin (7 t)

y^{^{'''}} - 3 y^{^{''}} - 4 y^{^{'}} = 0

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)