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Popular >

derivative of x^3e^{sqrt(x)}

Solution

\frac{d}{d x} (x^{3} e^{x})

Solution

3 e^{x} x^{2} + \frac{e ^{x} x ^{\frac{5}{2}}}{2}

Solution steps

\frac{d}{d x} (x^{3} e^{x})

Apply the Product Rule:

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

f = x^{3}, g = e^{x}

= \frac{d}{d x} (x^{3}) e^{x} + \frac{d}{d x} (e^{x}) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (e^{x}) = \frac{e ^{x}}{2 x}

= 3 x^{2} e^{x} + \frac{e ^{x}}{2 x} x^{3}

\frac{e ^{x}}{2 x} x^{3} = \frac{e ^{x} x ^{\frac{5}{2}}}{2}

= 3 e^{x} x^{2} + \frac{e ^{x} x ^{\frac{5}{2}}}{2}

Graph

Popular Examples

integral of 1/(e^{kx)}

\int \frac{1}{e ^{k x}} d x

y^{''}+y=0,y(0)=0,y(pi)=0

y^{^{''}} + y = 0, y (0) = 0, y (π) = 0

tangent of y=sqrt(2x+1)(4.3)tangent of

y = 2 x + 1 (4.3)

integral of x(x-1)^5

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

(\partial)/(\partial x)(y^{1/3}x^{2/3})

\frac{\partial}{\partial x} (y^{\frac{1}{3}} x^{\frac{2}{3}})

Frequently Asked Questions (FAQ)

What is the derivative of x^3e^{sqrt(x)} ?
The derivative of x^3e^{sqrt(x)} is 3e^{sqrt(x)}x^2+(e^{sqrt(x)}x^{5/2})/2
What is the first derivative of x^3e^{sqrt(x)} ?
The first derivative of x^3e^{sqrt(x)} is 3e^{sqrt(x)}x^2+(e^{sqrt(x)}x^{5/2})/2