What is the derivative of x-sin^2(x-4) ?

The derivative of x-sin^2(x-4) is -sin(2x)+1

What is the first derivative of x-sin^2(x-4) ?

The first derivative of x-sin^2(x-4) is -sin(2x)+1

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\frac{d}{d x} (x - sin^{2} (x) - 4)

- sin (2 x) + 1

Solution steps

\frac{d}{d x} (x - sin^{2} (x) - 4)

Apply the Sum/Difference Rule:

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

= \frac{d x}{d x} - \frac{d}{d x} (sin^{2} (x)) - \frac{d}{d x} (4)

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

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

\frac{d}{d x} (4) = 0

= 1 - sin (2 x) - 0

Simplify

= - sin (2 x) + 1

What is the derivative of x-sin^2(x-4) ?
The derivative of x-sin^2(x-4) is -sin(2x)+1
What is the first derivative of x-sin^2(x-4) ?
The first derivative of x-sin^2(x-4) is -sin(2x)+1