What is the derivative of 2sin(x+5cos(3pix)) ?

The derivative of 2sin(x+5cos(3pix)) is 2cos(x)-15pisin(3pix)

What is the first derivative of 2sin(x+5cos(3pix)) ?

The first derivative of 2sin(x+5cos(3pix)) is 2cos(x)-15pisin(3pix)

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\frac{d}{d x} (2 sin (x) + 5 cos (3 π x))

2 cos (x) - 15 π sin (3 π x)

Solution steps

\frac{d}{d x} (2 sin (x) + 5 cos (3 π x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 sin (x)) + \frac{d}{d x} (5 cos (3 π x))

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

\frac{d}{d x} (5 cos (3 π x)) = - 15 π sin (3 π x)

= 2 cos (x) - 15 π sin (3 π x)

What is the derivative of 2sin(x+5cos(3pix)) ?
The derivative of 2sin(x+5cos(3pix)) is 2cos(x)-15pisin(3pix)
What is the first derivative of 2sin(x+5cos(3pix)) ?
The first derivative of 2sin(x+5cos(3pix)) is 2cos(x)-15pisin(3pix)