What is the derivative of \sqrt[5]{(5x)/(8x-3)} ?

The derivative of \sqrt[5]{(5x)/(8x-3)} is -3/(5^{4/5)x^{4/5}(8x-3)^{6/5}}

What is the first derivative of \sqrt[5]{(5x)/(8x-3)} ?

The first derivative of \sqrt[5]{(5x)/(8x-3)} is -3/(5^{4/5)x^{4/5}(8x-3)^{6/5}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

- \frac{3}{5 ^{\frac{4}{5}} x ^{\frac{4}{5}} ( 8 x - 3 ) ^{\frac{6}{5}}}

Solution steps

Apply the chain rule:

\frac{1}{5 ( \frac{5 x}{8 x - 3} ) ^{\frac{4}{5}}} \frac{d}{d x} (\frac{5 x}{8 x - 3})

= \frac{1}{5 ( \frac{5 x}{8 x - 3} ) ^{\frac{4}{5}}} \frac{d}{d x} (\frac{5 x}{8 x - 3})

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

= \frac{1}{5 ( \frac{5 x}{8 x - 3} ) ^{\frac{4}{5}}} (- \frac{15}{( 8 x - 3 ) ^{2}})

Simplify

\frac{1}{5 ( \frac{5 x}{8 x - 3} ) ^{\frac{4}{5}}} (- \frac{15}{( 8 x - 3 ) ^{2}}) : - \frac{3}{5 ^{\frac{4}{5}} x ^{\frac{4}{5}} ( 8 x - 3 ) ^{\frac{6}{5}}}

= - \frac{3}{5 ^{\frac{4}{5}} x ^{\frac{4}{5}} ( 8 x - 3 ) ^{\frac{6}{5}}}

[1]

\int 17 (tan (x)) (ln (cos (x))) d x

f (t) = 4 sin (t)

\int \frac{9}{16 + 25 r ^{2}} d r

\frac{d y}{d t} - y = e^{t} + 12 e^{7 t}

What is the derivative of \sqrt[5]{(5x)/(8x-3)} ?
The derivative of \sqrt[5]{(5x)/(8x-3)} is -3/(5^{4/5)x^{4/5}(8x-3)^{6/5}}
What is the first derivative of \sqrt[5]{(5x)/(8x-3)} ?
The first derivative of \sqrt[5]{(5x)/(8x-3)} is -3/(5^{4/5)x^{4/5}(8x-3)^{6/5}}