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Popular >

derivative of 1/(sqrt(5-6x))

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 0 of (sin(x/5))/x

x \to 0 lim (\frac{sin ( \frac{x}{5} )}{x})

(dy)/(dx)=(2x(y-2))/(x^2+1),y(0)=4

\frac{d y}{d x} = \frac{2 x ( y - 2 )}{x ^{2} + 1}, y (0) = 4

y^{^{''''}} - 81 y = 0

(\partial)/(\partial x)(-e^{-x})

\frac{\partial}{\partial x} (- e^{- x})

derivative of (x^2-9x+8)/(x^2+9)derivative of

\frac{x ^{2} - 9 x + 8}{x ^{2} + 9}

Frequently Asked Questions (FAQ)

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