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Popular >

derivative of f(x)=(5x-5)(sqrt(x)+3)

Solution

derivative of

f (x) = (5 x - 5) (x + 3)

Solution

\frac{15 x - 5}{2 x} + 15

Solution steps

\frac{d}{d x} ((5 x - 5) (x + 3))

Apply the Product Rule:

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

f = 5 x - 5, g = x + 3

= \frac{d}{d x} (5 x - 5) (x + 3) + \frac{d}{d x} (x + 3) (5 x - 5)

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

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

= 5 (x + 3) + \frac{1}{2 x} (5 x - 5)

Simplify

5 (x + 3) + \frac{1}{2 x} (5 x - 5) : \frac{15 x - 5}{2 x} + 15

= \frac{15 x - 5}{2 x} + 15

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(5x-5)(sqrt(x)+3) ?
The derivative of f(x)=(5x-5)(sqrt(x)+3) is (15x-5)/(2sqrt(x))+15
What is the first derivative of f(x)=(5x-5)(sqrt(x)+3) ?
The first derivative of f(x)=(5x-5)(sqrt(x)+3) is (15x-5)/(2sqrt(x))+15