Question
Download Solution PDFIf \(\rm y=x^{\sec^2x}\times\frac{1}{x^{\tan^2x}}\), then \(\rm \frac{dy}{dx}=?\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\rm y=x^{\sec^2x}\times\frac{1}{x^{\tan^2x}}\)
Concept:
Use trigonometric identity \(\rm \sec^2x-\tan^2x=1\)
And use derivative rule \(\rm \frac{d}{dx}x^n=n x^{n-1}\)
Calculation:
\(\rm y=x^{\sec^2x}\times\frac{1}{x^{\tan^2x}}\)
\(\rm \implies y=x^{\sec^2x}\times x^{-\tan^2x}\)
\(\rm \implies y=x^{\sec^2x-\tan^2x}\)
\(\rm \implies y=x\)
Now differentiate with respect to \(\rm x\)
we get
\(\rm \frac{dy}{dx}=1\)
Hence the option (4) is correct.
Last updated on May 26, 2025
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