What is the derivative of sqrt(5x^3+2x^2+3) ?

The derivative of sqrt(5x^3+2x^2+3) is (15x^2+4x)/(2sqrt(5x^3+2x^2+3))

What is the first derivative of sqrt(5x^3+2x^2+3) ?

The first derivative of sqrt(5x^3+2x^2+3) is (15x^2+4x)/(2sqrt(5x^3+2x^2+3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

5 x^{3} + 2 x^{2} + 3

\frac{15 x ^{2} + 4 x}{2 5 x ^{3} + 2 x ^{2} + 3}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 x^{3} + 2 x^{2} + 3) = 15 x^{2} + 4 x

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

Simplify

\frac{1}{2 5 x ^{3} + 2 x ^{2} + 3} (15 x^{2} + 4 x) : \frac{15 x ^{2} + 4 x}{2 5 x ^{3} + 2 x ^{2} + 3}

= \frac{15 x ^{2} + 4 x}{2 5 x ^{3} + 2 x ^{2} + 3}

What is the derivative of sqrt(5x^3+2x^2+3) ?
The derivative of sqrt(5x^3+2x^2+3) is (15x^2+4x)/(2sqrt(5x^3+2x^2+3))
What is the first derivative of sqrt(5x^3+2x^2+3) ?
The first derivative of sqrt(5x^3+2x^2+3) is (15x^2+4x)/(2sqrt(5x^3+2x^2+3))