What is the derivative of (5+3xcos(x)) ?

The derivative of (5+3xcos(x)) is 3cos(x)-sin(x)(5+3x)

What is the first derivative of (5+3xcos(x)) ?

The first derivative of (5+3xcos(x)) is 3cos(x)-sin(x)(5+3x)

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

3 cos (x) - sin (x) (5 + 3 x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 5 + 3 x, g = cos (x)

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

\frac{d}{d x} (5 + 3 x) = 3

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

= 3 cos (x) + (- sin (x)) (5 + 3 x)

Simplify

= 3 cos (x) - sin (x) (5 + 3 x)

What is the derivative of (5+3xcos(x)) ?
The derivative of (5+3xcos(x)) is 3cos(x)-sin(x)(5+3x)
What is the first derivative of (5+3xcos(x)) ?
The first derivative of (5+3xcos(x)) is 3cos(x)-sin(x)(5+3x)