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Popular >

derivative of 5xsqrt(x)

Solution

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

Solution

\frac{15 x}{2}

Solution steps

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

Simplify

5 x x : 5 x^{\frac{3}{2}}

= \frac{d}{d x} (5 x^{\frac{3}{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (x^{\frac{3}{2}})

Apply the Power Rule:

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

= 5 \cdot \frac{3}{2} x^{\frac{3}{2} - 1}

Simplify

5 \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : \frac{15 x}{2}

= \frac{15 x}{2}

Popular Examples

derivative of 2cos(1/2 x)

\frac{d}{d x} (2 cos (\frac{1}{2} x))

integral from 0 to pi/4 of cos(x)

\int_{0}^{\frac{π}{4}} cos (x) d x

derivative of 20x^{-8}+5x^{-3}-7x^{-7}

\frac{d}{d x} (20 x^{- 8} + 5 x^{- 3} - 7 x^{- 7})

derivative of 1/(sqrt(x^2-9y^2))

\frac{d}{d x} (\frac{1}{x ^{2} - 9 y ^{2}})

derivative of (1-x^2^{10})

\frac{d}{d x} ((1 - x^{2})^{10})

Frequently Asked Questions (FAQ)

What is the derivative of 5xsqrt(x) ?
The derivative of 5xsqrt(x) is (15sqrt(x))/2
What is the first derivative of 5xsqrt(x) ?
The first derivative of 5xsqrt(x) is (15sqrt(x))/2