en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(8x^3-x^2)

Solution

\frac{d}{d x} (ln (8 x^{3} - x^{2}))

Solution

\frac{2 ( 12 x - 1 )}{x ( 8 x - 1 )}

Solution steps

\frac{d}{d x} (ln (8 x^{3} - x^{2}))

Apply the chain rule:

\frac{1}{8 x ^{3} - x ^{2}} \frac{d}{d x} (8 x^{3} - x^{2})

= \frac{1}{8 x ^{3} - x ^{2}} \frac{d}{d x} (8 x^{3} - x^{2})

\frac{d}{d x} (8 x^{3} - x^{2}) = 24 x^{2} - 2 x

= \frac{1}{8 x ^{3} - x ^{2}} (24 x^{2} - 2 x)

Simplify

\frac{1}{8 x ^{3} - x ^{2}} (24 x^{2} - 2 x) : \frac{2 ( 12 x - 1 )}{x ( 8 x - 1 )}

= \frac{2 ( 12 x - 1 )}{x ( 8 x - 1 )}

Graph

Popular Examples

(dy)/(e^{4y)}=e^{5t}dt

\frac{d y}{e ^{4 y}} = e^{5 t} d t

normal of y=8x^2+8,(2,40)normal of

y = 8 x^{2} + 8, (2, 40)

integral of (1+x)e^x

\int (1 + x) e^{x} d x

derivative of 13x^8 derivative of

13 x^{8}

derivative of 2^xln(2)derivative of

2^{x} ln (2)

Frequently Asked Questions (FAQ)

What is the derivative of ln(8x^3-x^2) ?
The derivative of ln(8x^3-x^2) is (2(12x-1))/(x(8x-1))
What is the first derivative of ln(8x^3-x^2) ?
The first derivative of ln(8x^3-x^2) is (2(12x-1))/(x(8x-1))