What is the derivative of f(x)=5x^{-3/5} ?

The derivative of f(x)=5x^{-3/5} is -3/(x^{8/5)}

What is the first derivative of f(x)=5x^{-3/5} ?

The first derivative of f(x)=5x^{-3/5} is -3/(x^{8/5)}

derivative of

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

- \frac{3}{x ^{\frac{8}{5}}}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

5 (- \frac{3}{5} x^{- \frac{3}{5} - 1}) : - \frac{3}{x ^{\frac{8}{5}}}

= - \frac{3}{x ^{\frac{8}{5}}}

t an g e n t y = x^{3} - 7 x^{2} + 8 x + 1

2 y^{^{''}} + y^{^{'}} - 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

\frac{\partial}{\partial y} (x \cdot e^{x \cdot y})

\frac{\partial}{\partial x} (- \frac{x}{( x ^{2} + y ^{2} )})

y^{^{''}} - 2 y^{^{'}} + y = 8 e^{x}

What is the derivative of f(x)=5x^{-3/5} ?
The derivative of f(x)=5x^{-3/5} is -3/(x^{8/5)}
What is the first derivative of f(x)=5x^{-3/5} ?
The first derivative of f(x)=5x^{-3/5} is -3/(x^{8/5)}