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

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

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

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

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

cos (x) + sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= cos (x) + sin (x)

\frac{d}{d x} (3 x^{2} + 5 x - 6)

\int \frac{sec ^{4} ( x )}{tan ^{2} ( x )} d x

\int \frac{3 x ^{3} + x}{x ^{4} + 2 x ^{2} + 1} d x

\frac{1}{( s ^{2} + 3 ) ( s ^{2} + 1 )}

\int \frac{sec ^{2} ( x )}{csc ( x )} d x

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