What is the derivative of x^3cos(x-9xsin(x)-9cos(x)) ?

The derivative of x^3cos(x-9xsin(x)-9cos(x)) is -x^3sin(x)+3x^2cos(x)-9xcos(x)

What is the first derivative of x^3cos(x-9xsin(x)-9cos(x)) ?

The first derivative of x^3cos(x-9xsin(x)-9cos(x)) is -x^3sin(x)+3x^2cos(x)-9xcos(x)

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\frac{d}{d x} (x^{3} cos (x) - 9 x sin (x) - 9 cos (x))

- x^{3} sin (x) + 3 x^{2} cos (x) - 9 x cos (x)

Solution steps

\frac{d}{d x} (x^{3} cos (x) - 9 x sin (x) - 9 cos (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3} cos (x)) - \frac{d}{d x} (9 x sin (x)) - \frac{d}{d x} (9 cos (x))

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

\frac{d}{d x} (9 x sin (x)) = 9 (sin (x) + x cos (x))

\frac{d}{d x} (9 cos (x)) = - 9 sin (x)

= 3 x^{2} cos (x) - x^{3} sin (x) - 9 (sin (x) + x cos (x)) - (- 9 sin (x))

Simplify

3 x^{2} cos (x) - x^{3} sin (x) - 9 (sin (x) + x cos (x)) - (- 9 sin (x)) : - x^{3} sin (x) + 3 x^{2} cos (x) - 9 x cos (x)

= - x^{3} sin (x) + 3 x^{2} cos (x) - 9 x cos (x)

x \to 0 lim (\frac{0}{x ^{4}})

- 3 x^{\frac{3}{2}} - 1

f (x) = \frac{9}{x}

\frac{d}{d x} (\frac{1}{x} + x - \frac{1}{x} - x)

y^{^{'}} = t - y

What is the derivative of x^3cos(x-9xsin(x)-9cos(x)) ?
The derivative of x^3cos(x-9xsin(x)-9cos(x)) is -x^3sin(x)+3x^2cos(x)-9xcos(x)
What is the first derivative of x^3cos(x-9xsin(x)-9cos(x)) ?
The first derivative of x^3cos(x-9xsin(x)-9cos(x)) is -x^3sin(x)+3x^2cos(x)-9xcos(x)