What is the derivative of (7x/(sqrt(x))) ?

The derivative of (7x/(sqrt(x))) is 7/(2sqrt(x))

What is the first derivative of (7x/(sqrt(x))) ?

The first derivative of (7x/(sqrt(x))) is 7/(2sqrt(x))

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\frac{d}{d x} (\frac{7 x}{x})

\frac{7}{2 x}

Solution steps

\frac{d}{d x} (\frac{7 x}{x})

Simplify

\frac{7 x}{x} : 7 x

= \frac{d}{d x} (7 x)

Take the constant out:

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

= 7 \frac{d}{d x} (x)

Apply radical rule:

a = a^{\frac{1}{2}}

= 7 \frac{d}{d x} (x^{\frac{1}{2}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 7 \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

7 \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{7}{2 x}

= \frac{7}{2 x}

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

(1 + x^{4}) d y + x (1 + 4 y^{2}) d x = 0

\int 2 ln (3 x) d x

csc (5 x) cot (5 x)

\frac{7}{x}

What is the derivative of (7x/(sqrt(x))) ?
The derivative of (7x/(sqrt(x))) is 7/(2sqrt(x))
What is the first derivative of (7x/(sqrt(x))) ?
The first derivative of (7x/(sqrt(x))) is 7/(2sqrt(x))