en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(5x^2-3x+4)

Solution

\frac{d}{d x} (ln (5 x^{2} - 3 x + 4))

Solution

\frac{10 x - 3}{5 x ^{2} - 3 x + 4}

Solution steps

\frac{d}{d x} (ln (5 x^{2} - 3 x + 4))

Apply the chain rule:

\frac{1}{5 x ^{2} - 3 x + 4} \frac{d}{d x} (5 x^{2} - 3 x + 4)

= \frac{1}{5 x ^{2} - 3 x + 4} \frac{d}{d x} (5 x^{2} - 3 x + 4)

\frac{d}{d x} (5 x^{2} - 3 x + 4) = 10 x - 3

= \frac{1}{5 x ^{2} - 3 x + 4} (10 x - 3)

Simplify

\frac{1}{5 x ^{2} - 3 x + 4} (10 x - 3) : \frac{10 x - 3}{5 x ^{2} - 3 x + 4}

= \frac{10 x - 3}{5 x ^{2} - 3 x + 4}

Popular Examples

derivative of (ln(x))/(x^4)derivative of

\frac{ln ( x )}{x ^{4}}

integral of (sqrt(x))/(x-36)

\int \frac{x}{x - 36} d x

tangent of y=4x-x^2 tangent of

y = 4 x - x^{2}

x*sin(x)*dx+cos(y)*dy=0

x \cdot sin (x) \cdot d x + cos (y) \cdot d y = 0

integral of y^2-2y+1

\int y^{2} - 2 y + 1 d y

Frequently Asked Questions (FAQ)

What is the derivative of ln(5x^2-3x+4) ?
The derivative of ln(5x^2-3x+4) is (10x-3)/(5x^2-3x+4)
What is the first derivative of ln(5x^2-3x+4) ?
The first derivative of ln(5x^2-3x+4) is (10x-3)/(5x^2-3x+4)