What is the derivative of y=(6sqrt(x)-2)(5sqrt(x)+7) ?

The derivative of y=(6sqrt(x)-2)(5sqrt(x)+7) is (30sqrt(x)+16)/(sqrt(x))

What is the first derivative of y=(6sqrt(x)-2)(5sqrt(x)+7) ?

The first derivative of y=(6sqrt(x)-2)(5sqrt(x)+7) is (30sqrt(x)+16)/(sqrt(x))

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derivative of

y = (6 x - 2) (5 x + 7)

\frac{30 x + 16}{x}

Solution steps

\frac{d}{d x} ((6 x - 2) (5 x + 7))

Apply the Product Rule:

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

f = 6 x - 2, g = 5 x + 7

= \frac{d}{d x} (6 x - 2) (5 x + 7) + \frac{d}{d x} (5 x + 7) (6 x - 2)

\frac{d}{d x} (6 x - 2) = \frac{3}{x}

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

= \frac{3}{x} (5 x + 7) + \frac{5}{2 x} (6 x - 2)

Simplify

\frac{3}{x} (5 x + 7) + \frac{5}{2 x} (6 x - 2) : \frac{30 x + 16}{x}

= \frac{30 x + 16}{x}

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What is the derivative of y=(6sqrt(x)-2)(5sqrt(x)+7) ?
The derivative of y=(6sqrt(x)-2)(5sqrt(x)+7) is (30sqrt(x)+16)/(sqrt(x))
What is the first derivative of y=(6sqrt(x)-2)(5sqrt(x)+7) ?
The first derivative of y=(6sqrt(x)-2)(5sqrt(x)+7) is (30sqrt(x)+16)/(sqrt(x))