What is the derivative of f(x)= 1/2 x^8 ?

The derivative of f(x)= 1/2 x^8 is 4x^7

What is the first derivative of f(x)= 1/2 x^8 ?

The first derivative of f(x)= 1/2 x^8 is 4x^7

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derivative of

f (x) = \frac{1}{2} x^{8}

4 x^{7}

Solution steps

\frac{d}{d x} (\frac{1}{2} x^{8})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (x^{8})

Apply the Power Rule:

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

= \frac{1}{2} \cdot 8 x^{8 - 1}

Simplify

\frac{1}{2} \cdot 8 x^{8 - 1} : 4 x^{7}

= 4 x^{7}

What is the derivative of f(x)= 1/2 x^8 ?
The derivative of f(x)= 1/2 x^8 is 4x^7
What is the first derivative of f(x)= 1/2 x^8 ?
The first derivative of f(x)= 1/2 x^8 is 4x^7