What is the derivative of Insqrt(9x) ?

The derivative of Insqrt(9x) is (3nI)/(2sqrt(x))

What is the first derivative of Insqrt(9x) ?

The first derivative of Insqrt(9x) is (3nI)/(2sqrt(x))

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\frac{d}{d x} (I n 9 x)

\frac{3 n I}{2 x}

Solution steps

\frac{d}{d x} (I n 9 x)

Simplify

I n 9 x : 3 n I x

= \frac{d}{d x} (3 n I x)

Treat

n, I

as a constant

Take the constant out:

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

= 3 n I \frac{d}{d x} (x)

Apply radical rule:

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

= 3 n I \frac{d}{d x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= 3 n I \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

3 n I \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{3 n I}{2 x}

= \frac{3 n I}{2 x}

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