What is the derivative of 4(2x-5^{-1/2}) ?

The derivative of 4(2x-5^{-1/2}) is -4/((2x-5)^{3/2)}

What is the first derivative of 4(2x-5^{-1/2}) ?

The first derivative of 4(2x-5^{-1/2}) is -4/((2x-5)^{3/2)}

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\frac{d}{d x} (4 (2 x - 5)^{- \frac{1}{2}})

- \frac{4}{( 2 x - 5 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (4 (2 x - 5)^{- \frac{1}{2}})

Take the constant out:

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

= 4 \frac{d}{d x} ((2 x - 5)^{- \frac{1}{2}})

Apply the chain rule:

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

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

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

= 4 (- \frac{1}{2 ( 2 x - 5 ) ^{\frac{3}{2}}} \cdot 2)

Simplify

4 (- \frac{1}{2 ( 2 x - 5 ) ^{\frac{3}{2}}} \cdot 2) : - \frac{4}{( 2 x - 5 ) ^{\frac{3}{2}}}

= - \frac{4}{( 2 x - 5 ) ^{\frac{3}{2}}}

\frac{\partial}{\partial x} (2 y sin (x))

\int_{0}^{3} e^{x} sin (x) d x

f (x) = \frac{x ^{3}}{3} + \frac{1}{4 x}

\int e^{x^{3}} x^{5} d x

s (t) = \frac{9}{t ^{2} + 9 t - 3}

What is the derivative of 4(2x-5^{-1/2}) ?
The derivative of 4(2x-5^{-1/2}) is -4/((2x-5)^{3/2)}
What is the first derivative of 4(2x-5^{-1/2}) ?
The first derivative of 4(2x-5^{-1/2}) is -4/((2x-5)^{3/2)}