What is the derivative of x^{5/2}e^x ?

The derivative of x^{5/2}e^x is (5e^xx^{3/2})/2+e^xx^{5/2}

What is the first derivative of x^{5/2}e^x ?

The first derivative of x^{5/2}e^x is (5e^xx^{3/2})/2+e^xx^{5/2}

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derivative of

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

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

Solution steps

\frac{d}{d x} (x^{\frac{5}{2}} e^{x})

Apply the Product Rule:

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

f = x^{\frac{5}{2}}, g = e^{x}

= \frac{d}{d x} (x^{\frac{5}{2}}) e^{x} + \frac{d}{d x} (e^{x}) x^{\frac{5}{2}}

\frac{d}{d x} (x^{\frac{5}{2}}) = \frac{5 x ^{\frac{3}{2}}}{2}

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

x \to 9 + lim (\frac{2}{x + 9})

e^{x + 2} + 2

\int - \frac{7}{5} x^{- 12} d x

\frac{d}{d x} (e^{c o s (x)} sin (x^{2} - x))

\int (3^{2} + x^{12}) d x

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