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Differentiate the following w.r.t.x: e2x-e-2xe2x+e-2x - Mathematics and Statistics

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प्रश्न

Differentiate the following w.r.t.x:

`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`

योग
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उत्तर

Let y = `(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`

= `(e^(2x) - 1/e^(2x))/(e^(2x) + 1/e^(2x))`

= `(e^(4x) - 1)/(e^(4x) + 1)`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"((e^(4x) - 1)/(e^(4x) + 1))`

= `((e^(4x) + 1)."d"/"dx"(e^(4x) - 1) - (e^(4x) - 1)."d"/"dx"(e^(4x) + 1))/(e^(4x) + 1)^2`

= `((e^(4x) + 1)[e^(4x)."d"/"dx"(4x) - 0] - (e^(4x) - 1)[e^(4x)."d"/"dx"(4x) + 0])/(e^(4x) + 1)^2`

= `((e^(4x) + 1).e^(4x) xx 4 - (e^(4x) - 1).e^(4x) xx 4)/(e^(4x) + 1)^2`

= `(4e^(4x)(e^(4x) + 1 - e^(4x) + 1))/(e^(4x) + 1)^2`

= `(4e^(4x)(cancel(e^(4x)) + 1 - cancel(e^(4x)) + 1))/(e^(4x) + 1)^2`

= `(4e^(4x)(1  + 1))/(e^(4x) + 1)^2`

= `(4e^(4x)(2))/(e^(4x) + 1)^2`

= `(8e^(4x))/(e^(4x) + 1)^2`.

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Differentiation
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Differentiation - Exercise 1.1 [पृष्ठ १२]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 1 Differentiation
Exercise 1.1 | Q 3.10 | पृष्ठ १२

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