What is the derivative of x-(x/2 ^2+(x/3)^3) ?

The derivative of x-(x/2 ^2+(x/3)^3) is 1-x/2+(x^2)/9

What is the first derivative of x-(x/2 ^2+(x/3)^3) ?

The first derivative of x-(x/2 ^2+(x/3)^3) is 1-x/2+(x^2)/9

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

1 - \frac{x}{2} + \frac{x ^{2}}{9}

Solution steps

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

Simplify

x - (\frac{x}{2})^{2} + (\frac{x}{3})^{3} : x - \frac{x ^{2}}{4} + \frac{x ^{3}}{27}

= \frac{d}{d x} (x - \frac{x ^{2}}{4} + \frac{x ^{3}}{27})

Apply the Sum/Difference Rule:

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

= \frac{d x}{d x} - \frac{d}{d x} (\frac{x ^{2}}{4}) + \frac{d}{d x} (\frac{x ^{3}}{27})

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

\frac{d}{d x} (\frac{x ^{2}}{4}) = \frac{x}{2}

\frac{d}{d x} (\frac{x ^{3}}{27}) = \frac{x ^{2}}{9}

= 1 - \frac{x}{2} + \frac{x ^{2}}{9}

What is the derivative of x-(x/2 ^2+(x/3)^3) ?
The derivative of x-(x/2 ^2+(x/3)^3) is 1-x/2+(x^2)/9
What is the first derivative of x-(x/2 ^2+(x/3)^3) ?
The first derivative of x-(x/2 ^2+(x/3)^3) is 1-x/2+(x^2)/9