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Popular >

derivative of (x+9)(9sqrt(x)+7)

Solution

derivative of

(x + 9) (9 x + 7)

Solution

\frac{27 x + 81}{2 x} + 7

Solution steps

\frac{d}{d x} ((x + 9) (9 x + 7))

Apply the Product Rule:

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

f = x + 9, g = 9 x + 7

= \frac{d}{d x} (x + 9) (9 x + 7) + \frac{d}{d x} (9 x + 7) (x + 9)

\frac{d}{d x} (x + 9) = 1

\frac{d}{d x} (9 x + 7) = \frac{9}{2 x}

= 1 \cdot (9 x + 7) + \frac{9}{2 x} (x + 9)

Simplify

1 \cdot (9 x + 7) + \frac{9}{2 x} (x + 9) : \frac{27 x + 81}{2 x} + 7

= \frac{27 x + 81}{2 x} + 7

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Frequently Asked Questions (FAQ)

What is the derivative of (x+9)(9sqrt(x)+7) ?
The derivative of (x+9)(9sqrt(x)+7) is (27x+81)/(2sqrt(x))+7
What is the first derivative of (x+9)(9sqrt(x)+7) ?
The first derivative of (x+9)(9sqrt(x)+7) is (27x+81)/(2sqrt(x))+7