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Popular >

derivative of x^5sqrt(x)

Solution

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

Solution

\frac{11 x ^{\frac{9}{2}}}{2}

Solution steps

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

Simplify

x^{5} x : x^{\frac{11}{2}}

= \frac{d}{d x} (x^{\frac{11}{2}})

Apply the Power Rule:

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

= \frac{11}{2} x^{\frac{11}{2} - 1}

Simplify

\frac{11}{2} x^{\frac{11}{2} - 1} : \frac{11 x ^{\frac{9}{2}}}{2}

= \frac{11 x ^{\frac{9}{2}}}{2}

Popular Examples

derivative of f(x)=3x-4 derivative of

f (x) = 3 x - 4

integral from-infinity to 1 of e^{4x}

\int_{- \infty}^{1} e^{4 x} d x

derivative of (x^2-2x-3/((x-1)^2))

\frac{d}{d x} (\frac{x ^{2} - 2 x - 3}{( x - 1 ) ^{2}})

sum from n=2 to infinity of 9/(n(n+2))

n = 2 \sum \infty \frac{9}{n ( n + 2 )}

derivative of x/(sqrt(1+x^2+x^4))

\frac{d}{d x} (\frac{x}{1 + x ^{2} + x ^{4}})

Frequently Asked Questions (FAQ)

What is the derivative of x^5sqrt(x) ?
The derivative of x^5sqrt(x) is (11x^{9/2})/2
What is the first derivative of x^5sqrt(x) ?
The first derivative of x^5sqrt(x) is (11x^{9/2})/2