What is the derivative of f(x)=(4x-3)(sqrt(x)+2) ?

The derivative of f(x)=(4x-3)(sqrt(x)+2) is (12x-3)/(2sqrt(x))+8

What is the first derivative of f(x)=(4x-3)(sqrt(x)+2) ?

The first derivative of f(x)=(4x-3)(sqrt(x)+2) is (12x-3)/(2sqrt(x))+8

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derivative of

f (x) = (4 x - 3) (x + 2)

\frac{12 x - 3}{2 x} + 8

Solution steps

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

Apply the Product Rule:

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

f = 4 x - 3, g = x + 2

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

\frac{d}{d x} (4 x - 3) = 4

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

= 4 (x + 2) + \frac{1}{2 x} (4 x - 3)

Simplify

4 (x + 2) + \frac{1}{2 x} (4 x - 3) : \frac{12 x - 3}{2 x} + 8

= \frac{12 x - 3}{2 x} + 8

What is the derivative of f(x)=(4x-3)(sqrt(x)+2) ?
The derivative of f(x)=(4x-3)(sqrt(x)+2) is (12x-3)/(2sqrt(x))+8
What is the first derivative of f(x)=(4x-3)(sqrt(x)+2) ?
The first derivative of f(x)=(4x-3)(sqrt(x)+2) is (12x-3)/(2sqrt(x))+8