What is the derivative of-9/((6x+3^{3/2)}) ?

The derivative of-9/((6x+3^{3/2)}) is (81)/((6x+3)^{5/2)}

What is the first derivative of-9/((6x+3^{3/2)}) ?

The first derivative of-9/((6x+3^{3/2)}) is (81)/((6x+3)^{5/2)}

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\frac{d}{d x} (- \frac{9}{( 6 x + 3 ) ^{\frac{3}{2}}})

\frac{81}{( 6 x + 3 ) ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (- \frac{9}{( 6 x + 3 ) ^{\frac{3}{2}}})

Take the constant out:

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

= - 9 \frac{d}{d x} (\frac{1}{( 6 x + 3 ) ^{\frac{3}{2}}})

Apply exponent rule:

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

= - 9 \frac{d}{d x} ((6 x + 3)^{- \frac{3}{2}})

Apply the chain rule:

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

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

\frac{d}{d x} (6 x + 3) = 6

= - 9 (- \frac{3}{2 ( 6 x + 3 ) ^{\frac{5}{2}}} \cdot 6)

Simplify

- 9 (- \frac{3}{2 ( 6 x + 3 ) ^{\frac{5}{2}}} \cdot 6) : \frac{81}{( 6 x + 3 ) ^{\frac{5}{2}}}

= \frac{81}{( 6 x + 3 ) ^{\frac{5}{2}}}

g (x) = x^{2} (1 - 2 x)

\frac{\partial}{\partial x} (x - y)

\frac{d}{d x} (sin (7 x + 2))

\int e^{2 x} sin (e^{x}) d x

\frac{\partial}{\partial x} (- cos (x y))

What is the derivative of-9/((6x+3^{3/2)}) ?
The derivative of-9/((6x+3^{3/2)}) is (81)/((6x+3)^{5/2)}
What is the first derivative of-9/((6x+3^{3/2)}) ?
The first derivative of-9/((6x+3^{3/2)}) is (81)/((6x+3)^{5/2)}