What is the derivative of a{r}(xcos(x)) ?

The derivative of a{r}(xcos(x)) is a(cos(x) derivative of {r}(x)-sin(x){r}(x))

What is the first derivative of a{r}(xcos(x)) ?

The first derivative of a{r}(xcos(x)) is a(cos(x) derivative of {r}(x)-sin(x){r}(x))

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\frac{d}{d x} (a r (x) cos (x))

a (cos (x) \frac{d}{d x} (r (x)) - sin (x) r (x))

Solution steps

\frac{d}{d x} (a r (x) cos (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= a \frac{d}{d x} (r (x) cos (x))

Apply the Product Rule:

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

f = r (x), g = cos (x)

= a (\frac{d}{d x} (r (x)) cos (x) + \frac{d}{d x} (cos (x)) r (x))

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

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

Simplify

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

\int_{0}^{5} x d x

\int \frac{1}{x ^{2} 10 x + 1} d x

\int e^{θ} sin (θ) d θ

n = 1 \sum \infty \frac{( ( - 3 ) ^{n - 1} )}{5 ^{n}}

\int 2 sin^{3} (x) d x

What is the derivative of a{r}(xcos(x)) ?
The derivative of a{r}(xcos(x)) is a(cos(x) derivative of {r}(x)-sin(x){r}(x))
What is the first derivative of a{r}(xcos(x)) ?
The first derivative of a{r}(xcos(x)) is a(cos(x) derivative of {r}(x)-sin(x){r}(x))