What is the derivative of (e^{5x}/(x^{15)}) ?

The derivative of (e^{5x}/(x^{15)}) is (5e^{5x}(x-3))/(x^{16)}

What is the first derivative of (e^{5x}/(x^{15)}) ?

The first derivative of (e^{5x}/(x^{15)}) is (5e^{5x}(x-3))/(x^{16)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{e ^{5 x}}{x ^{15}})

\frac{5 e ^{5 x} ( x - 3 )}{x ^{16}}

Solution steps

\frac{d}{d x} (\frac{e ^{5 x}}{x ^{15}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{5 x} ) x ^{15} - \frac{d}{d x} ( x ^{15} ) e ^{5 x}}{( x ^{15} ) ^{2}}

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

\frac{d}{d x} (x^{15}) = 15 x^{14}

= \frac{e ^{5 x} \cdot 5 x ^{15} - 15 x ^{14} e ^{5 x}}{( x ^{15} ) ^{2}}

Simplify

\frac{e ^{5 x} \cdot 5 x ^{15} - 15 x ^{14} e ^{5 x}}{( x ^{15} ) ^{2}} : \frac{5 e ^{5 x} ( x - 3 )}{x ^{16}}

= \frac{5 e ^{5 x} ( x - 3 )}{x ^{16}}

\frac{d}{d x} (b (x + a)^{3} + c)

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

x \to \infty lim (x \cdot 2)

\frac{\partial}{\partial x} (x^{4} + y^{4} + z^{4} - 4 x yz)

What is the derivative of (e^{5x}/(x^{15)}) ?
The derivative of (e^{5x}/(x^{15)}) is (5e^{5x}(x-3))/(x^{16)}
What is the first derivative of (e^{5x}/(x^{15)}) ?
The first derivative of (e^{5x}/(x^{15)}) is (5e^{5x}(x-3))/(x^{16)}