What is the derivative of 4xsqrt(x) ?

The derivative of 4xsqrt(x) is 6sqrt(x)

What is the first derivative of 4xsqrt(x) ?

The first derivative of 4xsqrt(x) is 6sqrt(x)

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\frac{d}{d x} (4 x x)

6 x

Solution steps

\frac{d}{d x} (4 x x)

Simplify

4 x x : 4 x^{\frac{3}{2}}

= \frac{d}{d x} (4 x^{\frac{3}{2}})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{\frac{3}{2}})

Apply the Power Rule:

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

= 4 \cdot \frac{3}{2} x^{\frac{3}{2} - 1}

Simplify

4 \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : 6 x

= 6 x

What is the derivative of 4xsqrt(x) ?
The derivative of 4xsqrt(x) is 6sqrt(x)
What is the first derivative of 4xsqrt(x) ?
The first derivative of 4xsqrt(x) is 6sqrt(x)