What is the derivative of f(x)= 1/2 x^2 ?

The derivative of f(x)= 1/2 x^2 is x

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

The first derivative of f(x)= 1/2 x^2 is x

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derivative of

f (x) = \frac{1}{2} x^{2}

x

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (x^{2})

Apply the Power Rule:

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

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

Simplify

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

= x

\frac{\partial}{\partial y} (ln (x^{8} y))

\frac{\partial}{\partial x} (x^{\frac{1}{4}} \cdot y^{\frac{3}{4}})

x \to π - lim (4 x)

\frac{\partial}{\partial x} (6 x^{- 3} - 8 x^{- 5})

\frac{d}{d x} (500 x - \frac{x ^{2}}{ln ( x + 300 )})

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