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Popular >

derivative of xe^{rx}

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

x^2y^{''}+2xy^'-2y=0

x^{2} y^{^{''}} + 2 x y^{^{'}} - 2 y = 0

tangent of f(x)=9e^x12x,\at x=0 tangent of

f (x) = 9 e^{x} 12 x, at x = 0

integral of (4x+2)(x^2+x-1)^5

\int (4 x + 2) (x^{2} + x - 1)^{5} d x

limit as x approaches+7 of 3/(x-7)

x \to + 7 lim (\frac{3}{x - 7})

integral of ((t^3-8t+1)/((2t)^4))

\int (\frac{t ^{3} - 8 t + 1}{( 2 t ) ^{4}}) d t

Frequently Asked Questions (FAQ)

What is the derivative of xe^{rx} ?
The derivative of xe^{rx} is e^{xr}+e^{xr}x(x(dr)/(dx)+r)
What is the first derivative of xe^{rx} ?
The first derivative of xe^{rx} is e^{xr}+e^{xr}x(x(dr)/(dx)+r)