What is the derivative of sqrt(x)(3x+1) ?

The derivative of sqrt(x)(3x+1) is (9x+1)/(2sqrt(x))

What is the first derivative of sqrt(x)(3x+1) ?

The first derivative of sqrt(x)(3x+1) is (9x+1)/(2sqrt(x))

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

\frac{9 x + 1}{2 x}

Solution steps

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

Apply the Product Rule:

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

f = x, g = 3 x + 1

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

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

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

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

Simplify

\frac{1}{2 x} (3 x + 1) + 3 x : \frac{9 x + 1}{2 x}

= \frac{9 x + 1}{2 x}

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

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

\int_{0}^{3} e^{2 x} d x

\int - 2 cot (x) d x

\frac{d}{d x} (x^{- \frac{1}{2}} cos (x))

What is the derivative of sqrt(x)(3x+1) ?
The derivative of sqrt(x)(3x+1) is (9x+1)/(2sqrt(x))
What is the first derivative of sqrt(x)(3x+1) ?
The first derivative of sqrt(x)(3x+1) is (9x+1)/(2sqrt(x))