Question

Find the first derivatives. f(x)=\sqrt{1-x^{2}}

Derivatives
ANSWERED
asked 2021-03-20
Find the first derivatives.
\(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{1}-{x}^{{{2}}}}}\)

Answers (1)

2021-03-22
Step 1
Given \(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{1}-{x}^{{{2}}}}}\)
We have to find the derivative of f(x)
Step 2
\(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{1}-{x}^{{{2}}}}}\)
\(\displaystyle{f}'{\left({x}\right)}={\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left[\sqrt{{{1}-{x}^{{{2}}}}}\right]}\ \ \ {\left[\because{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}\sqrt{{{x}}}={\frac{{{1}}}{{{2}\sqrt{{{x}}}}}}\right]}\)
\(\displaystyle={\frac{{{1}}}{{{2}\sqrt{{{1}-{x}^{{{2}}}}}}}}{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({1}-{x}^{{{2}}}\right)}\)
\(\displaystyle={\frac{{{1}}}{{{2}\sqrt{{{1}-{x}^{{{2}}}}}}}}{\left(-{2}{x}\right)}\)
\(\displaystyle={\frac{{-{x}}}{{\sqrt{{{1}-{x}^{{{2}}}}}}}}\)
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