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Popular >

derivative of f(x)=2x^{3/2}

Solution

derivative of

f (x) = 2 x^{\frac{3}{2}}

Solution

3 x^{\frac{1}{2}}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

= 3 x^{\frac{1}{2}}

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(dy)/(dx)=10+40x+10y+40xy

\frac{d y}{d x} = 10 + 40 x + 10 y + 40 x y

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=2x^{3/2} ?
The derivative of f(x)=2x^{3/2} is 3x^{1/2}
What is the first derivative of f(x)=2x^{3/2} ?
The first derivative of f(x)=2x^{3/2} is 3x^{1/2}