What is the derivative of g(x)=(2x-sqrt(x))(5x+2) ?

The derivative of g(x)=(2x-sqrt(x))(5x+2) is (-15x+40xsqrt(x)-2)/(2sqrt(x))+4

What is the first derivative of g(x)=(2x-sqrt(x))(5x+2) ?

The first derivative of g(x)=(2x-sqrt(x))(5x+2) is (-15x+40xsqrt(x)-2)/(2sqrt(x))+4

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derivative of

g (x) = (2 x - x) (5 x + 2)

\frac{- 15 x + 40 x x - 2}{2 x} + 4

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 x - x, g = 5 x + 2

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

\frac{d}{d x} (2 x - x) = 2 - \frac{1}{2 x}

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

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

Simplify

(2 - \frac{1}{2 x}) (5 x + 2) + 5 (2 x - x) : \frac{- 15 x + 40 x x - 2}{2 x} + 4

= \frac{- 15 x + 40 x x - 2}{2 x} + 4

What is the derivative of g(x)=(2x-sqrt(x))(5x+2) ?
The derivative of g(x)=(2x-sqrt(x))(5x+2) is (-15x+40xsqrt(x)-2)/(2sqrt(x))+4
What is the first derivative of g(x)=(2x-sqrt(x))(5x+2) ?
The first derivative of g(x)=(2x-sqrt(x))(5x+2) is (-15x+40xsqrt(x)-2)/(2sqrt(x))+4