What is the derivative of xsqrt(x+5) ?

The derivative of xsqrt(x+5) is (3x+10)/(2sqrt(x+5))

What is the first derivative of xsqrt(x+5) ?

The first derivative of xsqrt(x+5) is (3x+10)/(2sqrt(x+5))

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derivative of

x x + 5

\frac{3 x + 10}{2 x + 5}

Solution steps

\frac{d}{d x} (x x + 5)

Apply the Product Rule:

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

f = x, g = x + 5

= \frac{d x}{d x} x + 5 + \frac{d}{d x} (x + 5) x

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

\frac{d}{d x} (x + 5) = \frac{1}{2 x + 5}

= 1 \cdot x + 5 + \frac{1}{2 x + 5} x

Simplify

1 \cdot x + 5 + \frac{1}{2 x + 5} x : \frac{3 x + 10}{2 x + 5}

= \frac{3 x + 10}{2 x + 5}

f (x) = ln (\frac{x + 1}{x - 1})

\int x^{1} (2 + 3 x^{2})^{3} d x

(5 - 1) (5 - 4)

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

\int (x^{2} + 3) cos (2 x) d x

What is the derivative of xsqrt(x+5) ?
The derivative of xsqrt(x+5) is (3x+10)/(2sqrt(x+5))
What is the first derivative of xsqrt(x+5) ?
The first derivative of xsqrt(x+5) is (3x+10)/(2sqrt(x+5))