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Popular >

derivative of 2xsqrt(x+1)

Solution

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

Solution

\frac{3 x + 2}{x + 1}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x, g = x + 1

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

\frac{d x}{d x} = 1

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

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

Simplify

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

= \frac{3 x + 2}{x + 1}

Popular Examples

integral from-3 to 2 of (6-x-x^2)

\int_{- 3}^{2} (6 - x - x^{2}) d x

derivative of e^{2sin^2(x})

\frac{d}{d x} (e^{2 s i n^{2} (x)})

integral of (2/(x^3))

\int (\frac{2}{x ^{3}}) d x

tangent of f(x)=4x-4sqrt(x)tangent of

f (x) = 4 x - 4 x

(\partial)/(\partial x)(cos(-x))

\frac{\partial}{\partial x} (cos (- x))

Frequently Asked Questions (FAQ)

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