What is the derivative of 4x^{-1/8} ?

The derivative of 4x^{-1/8} is -1/(2x^{9/8)}

What is the first derivative of 4x^{-1/8} ?

The first derivative of 4x^{-1/8} is -1/(2x^{9/8)}

derivative of

4 x^{- \frac{1}{8}}

- \frac{1}{2 x ^{\frac{9}{8}}}

Solution steps

\frac{d}{d x} (4 x^{- \frac{1}{8}})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{- \frac{1}{8}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 4 (- \frac{1}{8} x^{- \frac{1}{8} - 1})

Simplify

4 (- \frac{1}{8} x^{- \frac{1}{8} - 1}) : - \frac{1}{2 x ^{\frac{9}{8}}}

= - \frac{1}{2 x ^{\frac{9}{8}}}

d er i v a t i v e (\frac{3 x ^{2}}{( 2 x + 4 )})^{3}

\frac{d y}{d x} = \frac{( 2 y + 5 ) ^{2}}{( 8 x + 9 ) ^{2}}

t an g e n t y = x^{2}, (2, 4)

x \to 3 lim (\frac{x ^{2} - 3 x}{x - 3})

x \to 0 lim ((e^{x} + x)^{\frac{5}{x}})

What is the derivative of 4x^{-1/8} ?
The derivative of 4x^{-1/8} is -1/(2x^{9/8)}
What is the first derivative of 4x^{-1/8} ?
The first derivative of 4x^{-1/8} is -1/(2x^{9/8)}