What is the derivative of-6sin(x-6xcos(x)+x^2sin(x)) ?

The derivative of-6sin(x-6xcos(x)+x^2sin(x)) is -12cos(x)+8xsin(x)+x^2cos(x)

What is the first derivative of-6sin(x-6xcos(x)+x^2sin(x)) ?

The first derivative of-6sin(x-6xcos(x)+x^2sin(x)) is -12cos(x)+8xsin(x)+x^2cos(x)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (6 sin (x)) = 6 cos (x)

\frac{d}{d x} (6 x cos (x)) = 6 (cos (x) - x sin (x))

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

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

Simplify

- 6 cos (x) - 6 (cos (x) - x sin (x)) + 2 x sin (x) + cos (x) x^{2} : - 12 cos (x) + 8 x sin (x) + x^{2} cos (x)

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

y = x^{8} f (x)

\int (1 + x)^{5} d x

x \to \infty lim (\frac{5 x}{5 x + 3 x ^{\frac{1}{x}}})

f (x) = 2 x - 3, 4, 0

f (x) = \frac{2}{x}, at x = 5

What is the derivative of-6sin(x-6xcos(x)+x^2sin(x)) ?
The derivative of-6sin(x-6xcos(x)+x^2sin(x)) is -12cos(x)+8xsin(x)+x^2cos(x)
What is the first derivative of-6sin(x-6xcos(x)+x^2sin(x)) ?
The first derivative of-6sin(x-6xcos(x)+x^2sin(x)) is -12cos(x)+8xsin(x)+x^2cos(x)