What is the derivative of 2/3 x^2-5x+3/x+7 ?

The derivative of 2/3 x^2-5x+3/x+7 is (4x)/3-3/(x^2)-5

What is the first derivative of 2/3 x^2-5x+3/x+7 ?

The first derivative of 2/3 x^2-5x+3/x+7 is (4x)/3-3/(x^2)-5

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\frac{d}{d x} (\frac{2}{3} x^{2} - 5 x + \frac{3}{x} + 7)

\frac{4 x}{3} - \frac{3}{x ^{2}} - 5

Solution steps

\frac{d}{d x} (\frac{2}{3} x^{2} - 5 x + \frac{3}{x} + 7)

Simplify

\frac{2}{3} x^{2} - 5 x + \frac{3}{x} + 7 : \frac{2 x ^{2}}{3} - 5 x + \frac{3}{x} + 7

= \frac{d}{d x} (\frac{2 x ^{2}}{3} - 5 x + \frac{3}{x} + 7)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{2 x ^{2}}{3}) - \frac{d}{d x} (5 x) + \frac{d}{d x} (\frac{3}{x}) + \frac{d}{d x} (7)

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

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

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

\frac{d}{d x} (7) = 0

= \frac{4 x}{3} - 5 - \frac{3}{x ^{2}} + 0

Simplify

= \frac{4 x}{3} - \frac{3}{x ^{2}} - 5

y = 20 - x, y = x, y = 1

y^{^{'}} = - a y (1 + 3 y)

\frac{\partial}{\partial y} (100 e^{- 2 x^{2} - y^{2}})

\int \frac{5 sin ^{3} ( x )}{cos ( x )} d x

\frac{\partial}{\partial x} (x^{3} y)

What is the derivative of 2/3 x^2-5x+3/x+7 ?
The derivative of 2/3 x^2-5x+3/x+7 is (4x)/3-3/(x^2)-5
What is the first derivative of 2/3 x^2-5x+3/x+7 ?
The first derivative of 2/3 x^2-5x+3/x+7 is (4x)/3-3/(x^2)-5