What is the derivative of x^7sqrt(x) ?

The derivative of x^7sqrt(x) is (15x^{13/2})/2

What is the first derivative of x^7sqrt(x) ?

The first derivative of x^7sqrt(x) is (15x^{13/2})/2

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

\frac{15 x ^{\frac{13}{2}}}{2}

Solution steps

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

Simplify

x^{7} x : x^{\frac{15}{2}}

= \frac{d}{d x} (x^{\frac{15}{2}})

Apply the Power Rule:

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

= \frac{15}{2} x^{\frac{15}{2} - 1}

Simplify

\frac{15}{2} x^{\frac{15}{2} - 1} : \frac{15 x ^{\frac{13}{2}}}{2}

= \frac{15 x ^{\frac{13}{2}}}{2}

What is the derivative of x^7sqrt(x) ?
The derivative of x^7sqrt(x) is (15x^{13/2})/2
What is the first derivative of x^7sqrt(x) ?
The first derivative of x^7sqrt(x) is (15x^{13/2})/2