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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

x \to π lim (tan (x))

y = x^{2} e^{x} - 2 x e^{x} + 7 e^{x}

x^{2} y^{^{''}} + 7 x y^{^{'}} + 8 y = \frac{6}{x}

f (x) = 8 x^{4}

\int \frac{( 6 + 6 x )}{1 + x ^{2}} d x

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