What is the derivative of sin(2x+3cos(2x)) ?

The derivative of sin(2x+3cos(2x)) is cos(2x)*2-6sin(2x)

What is the first derivative of sin(2x+3cos(2x)) ?

The first derivative of sin(2x+3cos(2x)) is cos(2x)*2-6sin(2x)

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\frac{d}{d x} (sin (2 x) + 3 cos (2 x))

cos (2 x) \cdot 2 - 6 sin (2 x)

Solution steps

\frac{d}{d x} (sin (2 x) + 3 cos (2 x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (sin (2 x)) + \frac{d}{d x} (3 cos (2 x))

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

\frac{d}{d x} (3 cos (2 x)) = - 6 sin (2 x)

= cos (2 x) \cdot 2 - 6 sin (2 x)

What is the derivative of sin(2x+3cos(2x)) ?
The derivative of sin(2x+3cos(2x)) is cos(2x)*2-6sin(2x)
What is the first derivative of sin(2x+3cos(2x)) ?
The first derivative of sin(2x+3cos(2x)) is cos(2x)*2-6sin(2x)