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Popular >

derivative of xe^{{r}(xx})

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{r (x) x} + e^{r (x) x} (x \frac{d}{d x} (r (x)) + r (x)) x

Simplify

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

Popular Examples

derivative of log_{5}(arccos(x^3-2))

\frac{d}{d x} (lo g_{5} (arccos (x^{3} - 2)))

(\partial)/(\partial x)(-2e^ysin(-x)+3y-4xy)

\frac{\partial}{\partial x} (- 2 e^{y} sin (- x) + 3 y - 4 x y)

(\partial)/(\partial x)(3(x^{1/3}+y^{1/3}))

\frac{\partial}{\partial x} (3 (x^{\frac{1}{3}} + y^{\frac{1}{3}}))

integral from 2 to 5 of 4/x

\int_{2}^{5} \frac{4}{x} d x

derivative of sqrt(120+x^3)derivative of

120 + x^{3}

Frequently Asked Questions (FAQ)

What is the derivative of xe^{{r}(xx}) ?
The derivative of xe^{{r}(xx}) is e^{x{r}(x)}+e^{x{r}(x)}x(x derivative of {r}(x)+{r}(x))
What is the first derivative of xe^{{r}(xx}) ?
The first derivative of xe^{{r}(xx}) is e^{x{r}(x)}+e^{x{r}(x)}x(x derivative of {r}(x)+{r}(x))