What is the derivative of f(x)=x^{5/2}e^x ?

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

What is the first derivative of f(x)=x^{5/2}e^x ?

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

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derivative of

f (x) = 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}}

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