What is the derivative of xsqrt(x+8) ?

The derivative of xsqrt(x+8) is (3x+16)/(2sqrt(x+8))

What is the first derivative of xsqrt(x+8) ?

The first derivative of xsqrt(x+8) is (3x+16)/(2sqrt(x+8))

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\frac{d}{d x} (x x + 8)

\frac{3 x + 16}{2 x + 8}

Solution steps

\frac{d}{d x} (x x + 8)

Apply the Product Rule:

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

f = x, g = x + 8

= \frac{d x}{d x} x + 8 + \frac{d}{d x} (x + 8) x

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

\frac{d}{d x} (x + 8) = \frac{1}{2 x + 8}

= 1 \cdot x + 8 + \frac{1}{2 x + 8} x

Simplify

1 \cdot x + 8 + \frac{1}{2 x + 8} x : \frac{3 x + 16}{2 x + 8}

= \frac{3 x + 16}{2 x + 8}

\int x^{3} - 8 x^{2} + 16 x + 1 d x

3 x^{\frac{1}{3}} - 5 x^{\frac{4}{3}}

\int e^{7 x + 1} d x

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

\frac{s}{s + a}

What is the derivative of xsqrt(x+8) ?
The derivative of xsqrt(x+8) is (3x+16)/(2sqrt(x+8))
What is the first derivative of xsqrt(x+8) ?
The first derivative of xsqrt(x+8) is (3x+16)/(2sqrt(x+8))