What is the derivative of cos(x-x*sin(x)) ?

The derivative of cos(x-x*sin(x)) is -2sin(x)-xcos(x)

What is the first derivative of cos(x-x*sin(x)) ?

The first derivative of cos(x-x*sin(x)) is -2sin(x)-xcos(x)

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\frac{d}{d x} (cos (x) - x \cdot sin (x))

- 2 sin (x) - x cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= - sin (x) - (sin (x) + x cos (x))

Simplify

= - 2 sin (x) - x cos (x)

\frac{1}{s + a}

x^{3} - 3 x^{2} + x - 5

\frac{\partial}{\partial x} (x^{3} + k y^{2} - 5 x y)

\int 3 x 1 - x^{2} d x

4 x y^{^{'}} = 2 x e^{x} - 4 y + 6 x^{2}

What is the derivative of cos(x-x*sin(x)) ?
The derivative of cos(x-x*sin(x)) is -2sin(x)-xcos(x)
What is the first derivative of cos(x-x*sin(x)) ?
The first derivative of cos(x-x*sin(x)) is -2sin(x)-xcos(x)