What is the derivative of 4sin(x-5cos(x)+x) ?

The derivative of 4sin(x-5cos(x)+x) is 4cos(x)+5sin(x)+1

What is the first derivative of 4sin(x-5cos(x)+x) ?

The first derivative of 4sin(x-5cos(x)+x) is 4cos(x)+5sin(x)+1

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\frac{d}{d x} (4 sin (x) - 5 cos (x) + x)

4 cos (x) + 5 sin (x) + 1

Solution steps

\frac{d}{d x} (4 sin (x) - 5 cos (x) + x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 sin (x)) - \frac{d}{d x} (5 cos (x)) + \frac{d x}{d x}

\frac{d}{d x} (4 sin (x)) = 4 cos (x)

\frac{d}{d x} (5 cos (x)) = - 5 sin (x)

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

= 4 cos (x) - (- 5 sin (x)) + 1

Simplify

= 4 cos (x) + 5 sin (x) + 1

What is the derivative of 4sin(x-5cos(x)+x) ?
The derivative of 4sin(x-5cos(x)+x) is 4cos(x)+5sin(x)+1
What is the first derivative of 4sin(x-5cos(x)+x) ?
The first derivative of 4sin(x-5cos(x)+x) is 4cos(x)+5sin(x)+1