What is the derivative of (1+xcos(x)) ?

The derivative of (1+xcos(x)) is cos(x)-sin(x)(1+x)

What is the first derivative of (1+xcos(x)) ?

The first derivative of (1+xcos(x)) is cos(x)-sin(x)(1+x)

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\frac{d}{d x} ((1 + x) cos (x))

cos (x) - sin (x) (1 + x)

Solution steps

\frac{d}{d x} ((1 + x) cos (x))

Apply the Product Rule:

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

f = 1 + x, g = cos (x)

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

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

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

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

Simplify

= cos (x) - sin (x) (1 + x)

f (t) = cos^{2} (e^{c o s^{2} (t)})

\int \frac{19}{x ^{2} + 1} d x

\frac{\partial}{\partial x} (7 e^{x})

\int \frac{x}{x - 2} d x

y^{^{'}} = \frac{x - 2}{y + 1}

What is the derivative of (1+xcos(x)) ?
The derivative of (1+xcos(x)) is cos(x)-sin(x)(1+x)
What is the first derivative of (1+xcos(x)) ?
The first derivative of (1+xcos(x)) is cos(x)-sin(x)(1+x)