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Popular >

derivative of sqrt(x^4+2x)

Solution

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

Solution

\frac{2 x ^{3} + 1}{x ^{4} + 2 x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2 x ^{3} + 1}{x ^{4} + 2 x}

Popular Examples

tangent of 1/(sqrt(4x))tangent of

\frac{1}{4 x}

integral from 4 to 9 of (x-sqrt(x))/x

\int_{4}^{9} \frac{x - x}{x} d x

integral of 3*sqrt(x+4)

\int 3 \cdot x + 4 d x

sum from n=0 to infinity of 4/(n^2)

n = 0 \sum \infty \frac{4}{n ^{2}}

(dy)/(dx)9x^2y+9y^2x=-9

\frac{d y}{d x} 9 x^{2} y + 9 y^{2} x = - 9

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x^4+2x) ?
The derivative of sqrt(x^4+2x) is (2x^3+1)/(sqrt(x^4+2x))
What is the first derivative of sqrt(x^4+2x) ?
The first derivative of sqrt(x^4+2x) is (2x^3+1)/(sqrt(x^4+2x))