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

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

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

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

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

\frac{2 x + 5}{2 x ( x + 5 )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x ( x + 5 )} (2 x + 5) : \frac{2 x + 5}{2 x ( x + 5 )}

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

\int ∣ y ∣ d y

x^{3} (x - 2)

y = cos^{2} (x)

\frac{\partial}{\partial x} (8 x^{2} + y^{2} - 7 y)

\frac{d}{d y} (4 x^{2} y^{3} + 2)

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