What is the derivative of (8x^5-15)/(x^4) ?

The derivative of (8x^5-15)/(x^4) is (4(2x^5+15))/(x^5)

What is the first derivative of (8x^5-15)/(x^4) ?

The first derivative of (8x^5-15)/(x^4) is (4(2x^5+15))/(x^5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{8 x ^{5} - 15}{x ^{4}}

\frac{4 ( 2 x ^{5} + 15 )}{x ^{5}}

Solution steps

\frac{d}{d x} (\frac{8 x ^{5} - 15}{x ^{4}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 x ^{5} - 15 ) x ^{4} - \frac{d}{d x} ( x ^{4} ) ( 8 x ^{5} - 15 )}{( x ^{4} ) ^{2}}

\frac{d}{d x} (8 x^{5} - 15) = 40 x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{40 x ^{4} x ^{4} - 4 x ^{3} ( 8 x ^{5} - 15 )}{( x ^{4} ) ^{2}}

Simplify

\frac{40 x ^{4} x ^{4} - 4 x ^{3} ( 8 x ^{5} - 15 )}{( x ^{4} ) ^{2}} : \frac{4 ( 2 x ^{5} + 15 )}{x ^{5}}

= \frac{4 ( 2 x ^{5} + 15 )}{x ^{5}}

What is the derivative of (8x^5-15)/(x^4) ?
The derivative of (8x^5-15)/(x^4) is (4(2x^5+15))/(x^5)
What is the first derivative of (8x^5-15)/(x^4) ?
The first derivative of (8x^5-15)/(x^4) is (4(2x^5+15))/(x^5)