en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(x^3-27x-5)

Solution

\frac{d}{d x} (ln (x^{3} - 27 x - 5))

Solution

\frac{3 x ^{2} - 27}{x ^{3} - 27 x - 5}

Solution steps

\frac{d}{d x} (ln (x^{3} - 27 x - 5))

Apply the chain rule:

\frac{1}{x ^{3} - 27 x - 5} \frac{d}{d x} (x^{3} - 27 x - 5)

= \frac{1}{x ^{3} - 27 x - 5} \frac{d}{d x} (x^{3} - 27 x - 5)

\frac{d}{d x} (x^{3} - 27 x - 5) = 3 x^{2} - 27

= \frac{1}{x ^{3} - 27 x - 5} (3 x^{2} - 27)

Simplify

\frac{1}{x ^{3} - 27 x - 5} (3 x^{2} - 27) : \frac{3 x ^{2} - 27}{x ^{3} - 27 x - 5}

= \frac{3 x ^{2} - 27}{x ^{3} - 27 x - 5}

Popular Examples

\frac{d y}{d x} = x - 2

laplacetransform 2(t-3)^2+14(t-3)+27 laplace transform

2 (t - 3)^{2} + 14 (t - 3) + 27

tangent of f(x)=2x^2-4x+5,(-1,11)tangent of

f (x) = 2 x^{2} - 4 x + 5, (- 1, 11)

((dy)/(dx))/2 =sqrt(y)

\frac{\frac{d y}{d x}}{2} = y

integral of 1/(2xlog_{5)(x)}

\int \frac{1}{2 x lo g _{5} ( x )} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(x^3-27x-5) ?
The derivative of ln(x^3-27x-5) is (3x^2-27)/(x^3-27x-5)
What is the first derivative of ln(x^3-27x-5) ?
The first derivative of ln(x^3-27x-5) is (3x^2-27)/(x^3-27x-5)