What is the derivative of 1/((sqrt(x+{n\))*x}) ?

The derivative of 1/((sqrt(x+{n\))*x}) is -(3x+2n)/(2x^2(x+n)sqrt(x+n))

What is the first derivative of 1/((sqrt(x+{n\))*x}) ?

The first derivative of 1/((sqrt(x+{n\))*x}) is -(3x+2n)/(2x^2(x+n)sqrt(x+n))

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\frac{d}{d x} \frac{1}{( x + { n } ) \cdot x}

- \frac{3 x + 2 n}{2 x ^{2} ( x + n ) x + n}

Solution steps

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

Apply exponent rule:

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

= \frac{d}{d x} ((x + n x)^{- 1})

Apply the chain rule:

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

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

\frac{d}{d x} (x + n x) = \frac{3 x + 2 n}{2 x + n}

= - \frac{1}{( x + n x ) ^{2}} \cdot \frac{3 x + 2 n}{2 x + n}

Simplify

- \frac{1}{( x + n x ) ^{2}} \cdot \frac{3 x + 2 n}{2 x + n} : - \frac{3 x + 2 n}{2 x ^{2} ( x + n ) x + n}

= - \frac{3 x + 2 n}{2 x ^{2} ( x + n ) x + n}

(3 x - 1)^{\frac{1}{3}}

(k + 2 l)^{\frac{1}{3}}

2 \cdot x \cdot e^{- 4 \cdot x^{3}}

x + a^{3}

f (x) = cos^{3} (x^{2}) 2

What is the derivative of 1/((sqrt(x+{n\))*x}) ?
The derivative of 1/((sqrt(x+{n\))*x}) is -(3x+2n)/(2x^2(x+n)sqrt(x+n))
What is the first derivative of 1/((sqrt(x+{n\))*x}) ?
The first derivative of 1/((sqrt(x+{n\))*x}) is -(3x+2n)/(2x^2(x+n)sqrt(x+n))