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Popular >

derivative of sqrt(x^3+4x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

y^{^{'}} + 2 y = 4

integral of ln(3t)

\int ln (3 t) d t

limit as x approaches 7 of x/(x^2+7)

x \to 7 lim (\frac{x}{x ^{2} + 7})

limit as x approaches infinity of 2*x

x \to \infty lim (2 \cdot x)

sum from n=1 to infinity of (n!)/(110^n)

n = 1 \sum \infty \frac{n !}{11 0 ^{n}}

Frequently Asked Questions (FAQ)

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