What is the derivative of f(x)=x^3sqrt(x) ?

The derivative of f(x)=x^3sqrt(x) is (7x^{5/2})/2

What is the first derivative of f(x)=x^3sqrt(x) ?

The first derivative of f(x)=x^3sqrt(x) is (7x^{5/2})/2

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derivative of

f (x) = x^{3} x

\frac{7 x ^{\frac{5}{2}}}{2}

Solution steps

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

Simplify

x^{3} x : x^{\frac{7}{2}}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{7}{2} x^{\frac{7}{2} - 1}

Simplify

\frac{7}{2} x^{\frac{7}{2} - 1} : \frac{7 x ^{\frac{5}{2}}}{2}

= \frac{7 x ^{\frac{5}{2}}}{2}

What is the derivative of f(x)=x^3sqrt(x) ?
The derivative of f(x)=x^3sqrt(x) is (7x^{5/2})/2
What is the first derivative of f(x)=x^3sqrt(x) ?
The first derivative of f(x)=x^3sqrt(x) is (7x^{5/2})/2