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Question
Differentiate the function with respect to x.
`sec(tan (sqrtx))`
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Solution
Let, y = `sec(tan (sqrtx))`
Differentiating both sides with respect to x,
`dy/dx = d/dx sec [tan (sqrtx)]`
= `sec (tan sqrtx) tan (tan sqrtx) d/dx tan sqrtx`
= `sec (tan sqrtx) tan (tan sqrtx) sec^2 sqrtx d/dx (sqrtx)`
= `sec (tan sqrtx) tan (tan sqrtx) sec^2 sqrtx * 1/2 x^(1/2-1)`
= `sec (tan sqrtx) tan (tan sqrtx) sec^2 sqrtx * 1/(2sqrtx)`
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