What is the derivative of 5x^7 ?

The derivative of 5x^7 is 35x^6

What is the first derivative of 5x^7 ?

The first derivative of 5x^7 is 35x^6

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\frac{d}{d x} (5 x^{7})

35 x^{6}

Solution steps

\frac{d}{d x} (5 x^{7})

Take the constant out:

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

= 5 \frac{d}{d x} (x^{7})

Apply the Power Rule:

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

= 5 \cdot 7 x^{7 - 1}

Simplify

= 35 x^{6}