What is the derivative of x+x^3 ?

The derivative of x+x^3 is 1+3x^2

What is the first derivative of x+x^3 ?

The first derivative of x+x^3 is 1+3x^2

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

1 + 3 x^{2}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= 1 + 3 x^{2}

\frac{d}{d x} (2 x + \frac{1}{3 x ^{3}})

x + \frac{x ^{3}}{3} - tan (x)

x \to \infty lim (\frac{( e ^{x} + e ^{- x} )}{2})

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

\frac{d}{d x} (4 sin (x) - 4 x cos (x))