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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x + 5) = 1

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

= 1 \cdot cos (x) + (- sin (x)) (x + 5)

Simplify

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

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