Answered: "Find the derivative of the following functionsy=ln⁡x4+x2" - Plainmath

Ashleigh Shaffer

Answered question

2022-03-24

Find the derivative of the following functions

y = \ln \sqrt{x^{4} + x^{2}}

Answer & Explanation

haiguetenteme7zyu

Beginner2022-03-25Added 13 answers

Step 1

y = \ln \sqrt{x^{4} + x^{2}}

\frac{d y}{d x} = \frac{d}{d x} (\ln \sqrt{x^{4} + x^{2}})

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

Step 2

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

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

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

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

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