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

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

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

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

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

x^{2} + 2 x - 1

Solution steps

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

Simplify

\frac{1}{3} x^{3} + x^{2} - x + 5 : \frac{x ^{3}}{3} + x^{2} - x + 5

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

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{d}{d x} (5) = 0

= x^{2} + 2 x - 1 + 0

Simplify

= x^{2} + 2 x - 1

n \to \infty lim (sin (\frac{nπ}{2}))

\int \frac{e ^{2 x}}{1 - e ^{2 x}} d x

x \to 3 - lim (\frac{x ^{2} - 9}{x - 3})

\frac{\partial}{\partial y} (cos (n x) e^{n y})

\int \frac{9}{x ^{2} x ^{2} + 36} d x

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