en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sqrt(5x^4+x^2)

Solution

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

Solution

\frac{10 x ^{2} + 1}{5 x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 x^{4} + x^{2}) = 20 x^{3} + 2 x

= \frac{1}{2 5 x ^{4} + x ^{2}} (20 x^{3} + 2 x)

Simplify

\frac{1}{2 5 x ^{4} + x ^{2}} (20 x^{3} + 2 x) : \frac{10 x ^{2} + 1}{5 x ^{2} + 1}

= \frac{10 x ^{2} + 1}{5 x ^{2} + 1}

Popular Examples

integral of (y^2)/((49-y^2)^{3/2)}

\int \frac{y ^{2}}{( 49 - y ^{2} ) ^{\frac{3}{2}}} d y

integral of (3x-6)e^{x^2-4x}

\int (3 x - 6) e^{x^{2} - 4 x} d x

derivative of cos^2(x)sin^2(x)derivative of

cos^{2} (x) sin^{2} (x)

sum from n=1 to infinity of (n!)/(105^n)

n = 1 \sum \infty \frac{n !}{10 5 ^{n}}

(\partial)/(\partial x)(x^2-3xy)

\frac{\partial}{\partial x} (x^{2} - 3 x y)

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(5x^4+x^2) ?
The derivative of sqrt(5x^4+x^2) is (10x^2+1)/(sqrt(5x^2+1))
What is the first derivative of sqrt(5x^4+x^2) ?
The first derivative of sqrt(5x^4+x^2) is (10x^2+1)/(sqrt(5x^2+1))