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

The derivative of a{r}(xcos(e^x)) is a(cos(e^x) derivative of {r}(x)-e^xsin(e^x){r}(x))

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

The first derivative of a{r}(xcos(e^x)) is a(cos(e^x) derivative of {r}(x)-e^xsin(e^x){r}(x))

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = r (x), g = cos (e^{x})

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

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

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

Simplify

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

\int_{0}^{4} 2 π (2 - y) (4 y^{2}) d y

\int (25 - x^{2} - 3) d x

n = 3 \sum \infty (\frac{3}{11})^{- n}

\int \frac{8}{x ln ( 2 x )} d x

\frac{\partial}{\partial x} (e^{- x y})

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