What is the derivative of (sqrt(x)+7)(sqrt(x)-4) ?

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

What is the first derivative of (sqrt(x)+7)(sqrt(x)-4) ?

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

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derivative of

(x + 7) (x - 4)

\frac{2 x + 3}{2 x}

Solution steps

\frac{d}{d x} ((x + 7) (x - 4))

Apply the Product Rule:

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

f = x + 7, g = x - 4

= \frac{d}{d x} (x + 7) (x - 4) + \frac{d}{d x} (x - 4) (x + 7)

\frac{d}{d x} (x + 7) = \frac{1}{2 x}

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

= \frac{1}{2 x} (x - 4) + \frac{1}{2 x} (x + 7)

Simplify

\frac{1}{2 x} (x - 4) + \frac{1}{2 x} (x + 7) : \frac{2 x + 3}{2 x}

= \frac{2 x + 3}{2 x}

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