What is the derivative of 1/(sqrt(6x+5)) ?

The derivative of 1/(sqrt(6x+5)) is -3/((6x+5)^{3/2)}

What is the first derivative of 1/(sqrt(6x+5)) ?

The first derivative of 1/(sqrt(6x+5)) is -3/((6x+5)^{3/2)}

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\frac{d}{d x} (\frac{1}{6 x + 5})

- \frac{3}{( 6 x + 5 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{6 x + 5})

Apply exponent rule:

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

= \frac{d}{d x} ((6 x + 5)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 6 x + 5 ) ^{\frac{3}{2}}} \frac{d}{d x} (6 x + 5)

= - \frac{1}{2 ( 6 x + 5 ) ^{\frac{3}{2}}} \frac{d}{d x} (6 x + 5)

\frac{d}{d x} (6 x + 5) = 6

= - \frac{1}{2 ( 6 x + 5 ) ^{\frac{3}{2}}} \cdot 6

Simplify

- \frac{1}{2 ( 6 x + 5 ) ^{\frac{3}{2}}} \cdot 6 : - \frac{3}{( 6 x + 5 ) ^{\frac{3}{2}}}

= - \frac{3}{( 6 x + 5 ) ^{\frac{3}{2}}}

\frac{\partial}{\partial y} (7 ln (2 x^{5} - 3 y))

\frac{1}{10 x ^{2}}, x, \frac{x}{10}

\frac{d y}{d x} = k y

\frac{\partial}{\partial x} (e^{x} \cdot cos (x))

9 (x^{6} - 2)^{5}

What is the derivative of 1/(sqrt(6x+5)) ?
The derivative of 1/(sqrt(6x+5)) is -3/((6x+5)^{3/2)}
What is the first derivative of 1/(sqrt(6x+5)) ?
The first derivative of 1/(sqrt(6x+5)) is -3/((6x+5)^{3/2)}