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Popular >

derivative of f(x)=sqrt(x)(2x+2)

Solution

derivative of

f (x) = x (2 x + 2)

Solution

\frac{3 x + 1}{x}

Solution steps

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

Apply the Product Rule:

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

f = x, g = 2 x + 2

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

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

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

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

Simplify

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

= \frac{3 x + 1}{x}

Popular Examples

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x \to 1 lim (\frac{5 - x ^{2}}{1 + x})

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\int 0.1

derivative of f(x)=4e^{x^{-3}}derivative of

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(\partial)/(\partial y)(sin(2x+3y))

\frac{\partial}{\partial y} (sin (2 x + 3 y))

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n = 0 \sum \infty (\frac{π}{3})^{n}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(x)(2x+2) ?
The derivative of f(x)=sqrt(x)(2x+2) is (3x+1)/(sqrt(x))
What is the first derivative of f(x)=sqrt(x)(2x+2) ?
The first derivative of f(x)=sqrt(x)(2x+2) is (3x+1)/(sqrt(x))