What is the derivative of 4/(\sqrt[4]{x}) ?

The derivative of 4/(\sqrt[4]{x}) is -1/(x^{5/4)}

What is the first derivative of 4/(\sqrt[4]{x}) ?

The first derivative of 4/(\sqrt[4]{x}) is -1/(x^{5/4)}

\frac{d}{d x} (\frac{4}{4 x})

- \frac{1}{x ^{\frac{5}{4}}}

Solution steps

\frac{d}{d x} (\frac{4}{4 x})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{4 x})

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= - \frac{1}{x ^{\frac{5}{4}}}

y^{^{''}} + 2 y^{^{'}} + 1 y = 0

\frac{\partial}{\partial y} (\frac{x}{( 1 + 2 x + 3 y )})

2 y^{^{''}} - 9 y^{^{'}} + 4 y = 0

f (x) = x^{6} e^{x}

y = e^{- 2 x} \cdot tan (8 x)

What is the derivative of 4/(\sqrt[4]{x}) ?
The derivative of 4/(\sqrt[4]{x}) is -1/(x^{5/4)}
What is the first derivative of 4/(\sqrt[4]{x}) ?
The first derivative of 4/(\sqrt[4]{x}) is -1/(x^{5/4)}