What is the derivative of f(x)=(x+sqrt(2x))(2x+1) ?

The derivative of f(x)=(x+sqrt(2x))(2x+1) is 4x+3sqrt(2)sqrt(x)+1/(sqrt(2)\sqrt{x)}+1

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

The first derivative of f(x)=(x+sqrt(2x))(2x+1) is 4x+3sqrt(2)sqrt(x)+1/(sqrt(2)\sqrt{x)}+1

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derivative of

f (x) = (x + 2 x) (2 x + 1)

4 x + 32 x + \frac{1}{2 x} + 1

Solution steps

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

Simplify

(x + 2 x) (2 x + 1) : (x + 2 x) (2 x + 1)

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

Apply the Product Rule:

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

f = x + 2 x, g = 2 x + 1

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

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

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

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

Simplify

(1 + \frac{1}{2 x}) (2 x + 1) + 2 (x + 2 x) : 4 x + 32 x + \frac{1}{2 x} + 1

= 4 x + 32 x + \frac{1}{2 x} + 1

What is the derivative of f(x)=(x+sqrt(2x))(2x+1) ?
The derivative of f(x)=(x+sqrt(2x))(2x+1) is 4x+3sqrt(2)sqrt(x)+1/(sqrt(2)\sqrt{x)}+1
What is the first derivative of f(x)=(x+sqrt(2x))(2x+1) ?
The first derivative of f(x)=(x+sqrt(2x))(2x+1) is 4x+3sqrt(2)sqrt(x)+1/(sqrt(2)\sqrt{x)}+1