What is the derivative of (x^3-x^2+1/5) ?

The derivative of (x^3-x^2+1/5) is 1/5 (3x^2-2x)

What is the first derivative of (x^3-x^2+1/5) ?

The first derivative of (x^3-x^2+1/5) is 1/5 (3x^2-2x)

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\frac{d}{d x} (\frac{x ^{3} - x ^{2} + 1}{5})

\frac{1}{5} (3 x^{2} - 2 x)

Solution steps

\frac{d}{d x} (\frac{x ^{3} - x ^{2} + 1}{5})

Take the constant out:

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

= \frac{1}{5} \frac{d}{d x} (x^{3} - x^{2} + 1)

Apply the Sum/Difference Rule:

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

= \frac{1}{5} (\frac{d}{d x} (x^{3}) - \frac{d}{d x} (x^{2}) + \frac{d}{d x} (1))

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

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

\frac{d}{d x} (1) = 0

= \frac{1}{5} (3 x^{2} - 2 x + 0)

Simplify

= \frac{1}{5} (3 x^{2} - 2 x)

What is the derivative of (x^3-x^2+1/5) ?
The derivative of (x^3-x^2+1/5) is 1/5 (3x^2-2x)
What is the first derivative of (x^3-x^2+1/5) ?
The first derivative of (x^3-x^2+1/5) is 1/5 (3x^2-2x)