What is the derivative of sin(x+3cos(x)) ?

The derivative of sin(x+3cos(x)) is cos(x)-3sin(x)

What is the first derivative of sin(x+3cos(x)) ?

The first derivative of sin(x+3cos(x)) is cos(x)-3sin(x)

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\frac{d}{d x} (sin (x) + 3 cos (x))

cos (x) - 3 sin (x)

Solution steps

\frac{d}{d x} (sin (x) + 3 cos (x))

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (3 cos (x)) = - 3 sin (x)

= cos (x) - 3 sin (x)

\int cot (\frac{1}{2} x) d x

\int x^{3} 5 - x^{2} d x

4 x y^{2} + \frac{d y}{d x} = 5 x^{4} y^{2}

\int (e^{y} + 4)^{5} e^{y} d y

\int - \frac{2}{25} x + 45 d x

What is the derivative of sin(x+3cos(x)) ?
The derivative of sin(x+3cos(x)) is cos(x)-3sin(x)
What is the first derivative of sin(x+3cos(x)) ?
The first derivative of sin(x+3cos(x)) is cos(x)-3sin(x)