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

The derivative of cos(x-sin(x)) is -sin(x)-cos(x)

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

The first derivative of cos(x-sin(x)) is -sin(x)-cos(x)

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

- sin (x) - cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= - sin (x) - cos (x)

\frac{d y}{d x} = x^{9} + 1

t^{2} \frac{d y}{d t} + 4 t y - y^{3} = 0, y (1) = \frac{3}{2}

y = \frac{3}{sin ( x ) + cos ( x )}

\int \frac{48}{36 - x ^{2}} d x

\frac{d}{d x} (\frac{( x + b ) ( x - a )}{( x - b )})

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