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Popular >

derivative of (sqrt(x^2+1)/(\sqrt[3]{x^2+1)})

Solution

Solution

\frac{x}{3 ( x ^{2} + 1 ) ^{\frac{5}{6}}}

Solution steps

Simplify

Apply the chain rule:

\frac{1}{6 ( x ^{2} + 1 ) ^{\frac{5}{6}}} \frac{d}{d x} (x^{2} + 1)

= \frac{1}{6 ( x ^{2} + 1 ) ^{\frac{5}{6}}} \frac{d}{d x} (x^{2} + 1)

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

= \frac{1}{6 ( x ^{2} + 1 ) ^{\frac{5}{6}}} \cdot 2 x

Simplify

\frac{1}{6 ( x ^{2} + 1 ) ^{\frac{5}{6}}} \cdot 2 x : \frac{x}{3 ( x ^{2} + 1 ) ^{\frac{5}{6}}}

= \frac{x}{3 ( x ^{2} + 1 ) ^{\frac{5}{6}}}

Popular Examples

integral of (x^3+3)^{1/4}x^5

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

integral of 3(x+5)e^{4x}

\int 3 (x + 5) e^{4 x} d x

derivative of (log_{10}(x)^2)

\frac{d}{d x} ((lo g_{10} (x))^{2})

f(x)=x^2-2x-2sin(x-2)

f (x) = x^{2} - 2 x - 2 sin (x - 2)

limit as x approaches 1-of (2x+1)/(x-1)

x \to 1 - lim (\frac{2 x + 1}{x - 1})

Frequently Asked Questions (FAQ)

What is the derivative of (sqrt(x^2+1)/(\sqrt[3]{x^2+1)}) ?
The derivative of (sqrt(x^2+1)/(\sqrt[3]{x^2+1)}) is x/(3(x^2+1)^{5/6)}
What is the first derivative of (sqrt(x^2+1)/(\sqrt[3]{x^2+1)}) ?
The first derivative of (sqrt(x^2+1)/(\sqrt[3]{x^2+1)}) is x/(3(x^2+1)^{5/6)}