What is the derivative of f(x)=x^{9/2}e^x ?

The derivative of f(x)=x^{9/2}e^x is (9e^xx^{7/2})/2+e^xx^{9/2}

What is the first derivative of f(x)=x^{9/2}e^x ?

The first derivative of f(x)=x^{9/2}e^x is (9e^xx^{7/2})/2+e^xx^{9/2}

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derivative of

f (x) = x^{\frac{9}{2}} e^{x}

\frac{9 e ^{x} x ^{\frac{7}{2}}}{2} + e^{x} x^{\frac{9}{2}}

Solution steps

\frac{d}{d x} (x^{\frac{9}{2}} e^{x})

Apply the Product Rule:

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

f = x^{\frac{9}{2}}, g = e^{x}

= \frac{d}{d x} (x^{\frac{9}{2}}) e^{x} + \frac{d}{d x} (e^{x}) x^{\frac{9}{2}}

\frac{d}{d x} (x^{\frac{9}{2}}) = \frac{9 x ^{\frac{7}{2}}}{2}

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

= \frac{9 x ^{\frac{7}{2}}}{2} e^{x} + e^{x} x^{\frac{9}{2}}

Multiply fractions:

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

= \frac{9 e ^{x} x ^{\frac{7}{2}}}{2} + e^{x} x^{\frac{9}{2}}

(- 2, - 6), (0, 6)

\int (6 x) d x

x \to 0 lim ((1 + \frac{1}{2 x})^{x})

1 - t

\int_{0}^{1} \frac{3 t ^{2}}{1 + t ^{3}} d t

What is the derivative of f(x)=x^{9/2}e^x ?
The derivative of f(x)=x^{9/2}e^x is (9e^xx^{7/2})/2+e^xx^{9/2}
What is the first derivative of f(x)=x^{9/2}e^x ?
The first derivative of f(x)=x^{9/2}e^x is (9e^xx^{7/2})/2+e^xx^{9/2}