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

The derivative of sin(x)cos(x)-sin^2(x)+x is cos(2x)-sin(2x)+1

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

The first derivative of sin(x)cos(x)-sin^2(x)+x is cos(2x)-sin(2x)+1

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derivative of

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

cos (2 x) - sin (2 x) + 1

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d x}{d x} = 1

= cos (2 x) - sin (2 x) + 1

What is the derivative of sin(x)cos(x)-sin^2(x)+x ?
The derivative of sin(x)cos(x)-sin^2(x)+x is cos(2x)-sin(2x)+1
What is the first derivative of sin(x)cos(x)-sin^2(x)+x ?
The first derivative of sin(x)cos(x)-sin^2(x)+x is cos(2x)-sin(2x)+1