What is the derivative of x+x^5 ?

The derivative of x+x^5 is 1+5x^4

What is the first derivative of x+x^5 ?

The first derivative of x+x^5 is 1+5x^4

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

1 + 5 x^{4}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{5}) = 5 x^{4}

= 1 + 5 x^{4}